<?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:blogger='http://schemas.google.com/blogger/2008' xmlns:georss='http://www.georss.org/georss' xmlns:gd="http://schemas.google.com/g/2005" xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-7402096489957706142</id><updated>2026-04-08T05:38:11.857-07:00</updated><category term="8051 projects using ldr"/><category term="8051c with peripherals"/><category term="ANALOG SIGNALS"/><category term="ANALOG SIGNALS AND LINEAR AMPLIFIERS"/><category term="Ahrefs"/><category term="Averages and Mixtures problems"/><category term="Averages problems"/><category term="Backlink watch"/><category term="Dofollow Backlink Checker"/><category term="How  They Are Applicable  In Electronics"/><category term="Innovative Engineering Projects"/><category term="LINEAR AMPLIFIERS"/><category term="Link diagnosis"/><category term="New Electronic Inventions"/><category term="Robots Header Tags in blogger"/><category term="Robots.txt Settings for Blogger"/><category term="Sitemap"/><category term="THE BIPOLAR LINEAR AMPLIFIER"/><category term="YOgesh sharma"/><category term="adc0808 interfacing"/><category term="analog circuits"/><category term="average problems"/><category term="average questions"/><category term="bipolar transistor biasing"/><category term="bipolar transistor characteristics"/><category term="bipolar transistor tutorial"/><category term="capacitor"/><category term="capacitor calculation"/><category term="easy circuit"/><category term="electronics projects"/><category term="electronics4projects"/><category term="formula for capacitance calculator"/><category term="get high PR backlinks"/><category term="how to get high ranking in google"/><category term="how to increase backlinks"/><category term="how to interface 8051 with adc"/><category term="how to use blogger"/><category term="ldr light system"/><category term="ldr sensor for color detction"/><category term="ldr sensor using micro controller"/><category term="ldr with color sensor"/><category term="led with sensor"/><category term="microcontroller with adc0808"/><category term="npn bipolar transistor"/><category term="online back link checker"/><category term="online seo check tools"/><category term="online site seo explore"/><category term="pnp bipolar transistor"/><category term="questions for time and work"/><category term="questions on time and work"/><category term="search engine optimization"/><category term="sensors for projects"/><category term="seo checking tolls"/><category term="seo for blogger"/><category term="seo friendly website"/><category term="seo tolls"/><category term="series capacitor calculator parallel"/><category term="short tricks for time and work questions"/><category term="site seo checker using google"/><category term="street light"/><category term="street light circuit"/><category term="street light using transistor"/><category term="time and work"/><category term="time and work questions"/><category term="using op-amp color sensor"/><category term="website seo checker"/><title type='text'>Innovative  Engineering Projects</title><subtitle type='html'>Electronics4projects blog for new Innovative Engineering Projects. In this site all about electronics projects, circuits, how to design, innovative ideas, and many more.In this site study material for 8051 microcontroller, sensors, adc0808, adc0404, 8051c, proteus simulation,robotics, automation projects, embedded system projects, easy project for 4th year students, .This blog contains all about electronics circuits in a new modern circuit design and totally practical things</subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>14</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-5459693038966211597</id><published>2014-03-27T04:33:00.000-07:00</published><updated>2014-03-27T04:33:20.655-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="online seo check tools"/><category scheme="http://www.blogger.com/atom/ns#" term="online site seo explore"/><category scheme="http://www.blogger.com/atom/ns#" term="seo checking tolls"/><category scheme="http://www.blogger.com/atom/ns#" term="seo tolls"/><category scheme="http://www.blogger.com/atom/ns#" term="site seo checker using google"/><category scheme="http://www.blogger.com/atom/ns#" term="website seo checker"/><title type='text'>Top Seo Tolls For Blogger | Seo Tolls for blogs </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;Best seo online tolls for seo&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;SEO stands for&amp;nbsp;&lt;/span&gt;Search Engine Optimization&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&amp;nbsp;and it is a brilliant thing for Bloggers and Webmasters to drive the real unlimited traffic from search engines. There are many basic and advanced things for SEO which we learn step by step and also implement them on our blogs like&amp;nbsp;&lt;/span&gt;optimizing template&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;,&amp;nbsp;&lt;/span&gt;adding meta descriptions&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;,&amp;nbsp;&lt;/span&gt;creating robots.txt file&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;,&amp;nbsp;&lt;/span&gt;submitting sitemap&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&amp;nbsp;and many more. Previously, We&#39;ve published many articles on SEO which can be found in&amp;nbsp;&lt;/span&gt;SEO Page&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&amp;nbsp;and now we&#39;re going to discuss about another topic of SEO. In this post, we&#39;re going to share the top 20 best free SEO tools for bloggers which can be helpful to drive more traffic and perform better in SERPs.&lt;/span&gt;&lt;br style=&quot;background-color: white; color: #555555; line-height: 24px;&quot; /&gt;&lt;a href=&quot;&quot; name=&quot;more&quot; style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&lt;/a&gt;&lt;span style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;1. Google Webmaster Tools&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Google Webmaster Tools allows you to submit the whole sitemap of your blog/site to Google for the index in its search engine. Once the sitemap the completely indexed then you blog will be appearing in Google search and through that you can receive organic traffic. It also has advanced features by which you can track the most popular keywords from which you&#39;re getting traffic and all other information about the traffic which is coming from Google search engine. You can also calculate the backlinks with this tool.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;2. Bing Webmaster Tools&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Just similar as Google Webmaster Tools, Bing is another search engine which is second most popular across the world. Through this tool, you can submit sitemap to Bing search engine and easily get traffic from there. It also helps you to optimize your blog for search engine better than previous. This is almost same with the above tool just the search engine is changed.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;3. Google Analytics&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Google Analytics&amp;nbsp;is one of the most popular tool to get the accurate and real statistics data about the visitors of your blog/site. There are many features in this tool that&#39;s why it is known as best. It counts the pageviews, daily visitors, monthly visitors of your blog. Bounce rate, geographical location of visitors, trackbacks, real-time (live) visitors, information of paid and free keywords and much more things are also available in this tool just free.&amp;nbsp;Install Google Analytics&amp;nbsp;in your blog now!&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;4. Google Keyword Planner&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;After Google Analytics,&amp;nbsp;&lt;a href=&quot;https://adwords.google.com/ko/KeywordPlanner/Home&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Keyword Planner&lt;/a&gt;&amp;nbsp;is also a useful tool for bloggers to get better ranking in SERPs. This is a keyword research tool by which you can decide better keyword for your content. Simply, with this tool, you can know that how much time a single keyword in searched in Google in the single month. You should target such keyword which may have high searches monthly and after that you can be able to get good traffic from search engines.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;5. Google PageSpeed Insights&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;https://developers.google.com/speed/pagespeed/insights/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Google PageSpeed Insights&lt;/a&gt;&amp;nbsp;- This is another free SEO tool provided by Google which helps you to know the page speed or loading speed of your blog. Every blogger and webmaster wants to&amp;nbsp;reduce the loading time of his blog/site&amp;nbsp;and this tool can be helpful at the time because this doesn&#39;t only calculate the loading time but also finds and provide you some tips by which you can&amp;nbsp;easily speed up your blog.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;6. Google Structured Data Testing Tool&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;As the days are passing, Google is trying to make it&#39;s search engine more easy and useful with correct result. You guys may be noticing that slowly slowly Google is changing design or view of search results. So, this is&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;a href=&quot;http://www.google.com/webmasters/tools/richsnippets&quot; style=&quot;color: #2aa4cf; font-family: Georgia, &#39;Times New Roman&#39;, serif; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Google structured data testing tool&lt;/a&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;which helps you to know that how your blog appears in search results. After testing, it also gives you some tips to appear your blog beautiful in search results.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;7. Google Trends&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://www.google.com/trends/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Google Trends&lt;/a&gt;&amp;nbsp;can also be helpful for bloggers to do better keyword research because this tool helps to know that what&#39;s trending in the current days, which topic is most popular in the current and how much time it is search and also from where it is searched. It also gives more advanced information. We can also search the custom keywords with this tool and easily get information about these custom keywords.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;8. Keyword Density Checker&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Keyword Density also plays role in search engine optimization and&amp;nbsp;&lt;a href=&quot;http://www.live-keyword-analysis.com/&quot; rel=&quot;nofollow&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Keyword Density Checker&lt;/a&gt;&amp;nbsp;tool can be helpful for us bloggers. For normal and proper SEO, we should do only 2-4% keyword density in our articles which will help us to&amp;nbsp;get better ranking in search engines&amp;nbsp;but if we write more than limit then there is chance to be penalized byGoogle penguin&amp;nbsp;which will decrease our organic traffic.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;9. SEOquake&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;
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&lt;a href=&quot;http://www.seoquake.com/&quot; rel=&quot;nofollow&quot; style=&quot;color: #2aa4cf; font-family: Georgia, &#39;Times New Roman&#39;, serif; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;SEOquake&lt;/a&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;is most popular free SEO tool which is a extension or plugin for our web browers like Google Chrome, Firefox and Opera. After installing this tool, whenever you will open any webpage in your browser, a bar will appear which will be having SEO information for that webpage. It consists of Alexa Rank, Page Rank, Domain Authority, Backlinks, Indexed Pages, Page Authority and much more.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;10. Open Site Explorer&lt;/span&gt;&lt;/h3&gt;
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&lt;a href=&quot;http://www.opensiteexplorer.org/&quot; rel=&quot;nofollow&quot; style=&quot;color: #2aa4cf; font-family: Georgia, &#39;Times New Roman&#39;, serif; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Open Site Explorer&lt;/a&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;is a website explorer which gives SEO information for the particular given domain. Through this tool, you can know the Domain and Page authority of any domain name, counts the backlinks and also gives more information. This tool also contains the premium version which is not free but free version also gives good result.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;11. Ahrefs&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;Ahrefs is a backlink checker and site explorer tool by which you can easily check the backlinks of your blog. The total number of backlinks,&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;kind of backlinks&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;such as&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;&amp;nbsp;&lt;/span&gt;nofollow and dofollow&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif;&quot;&gt;, the location of backlinks and much more you can get from this tool. This also has premium version which will be provide more better data but free is also fine for blogger.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;12. Alexa&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Alexa is a well known algorithm for SEO Analysts and Bloggers. It is owned by amazon company and Alexa gives the rank to the every website on the internet. Most of bloggers try to improve their alexa rank which shows that the blog is going better and it is better than other webs on the internet. Alexa doesn&#39;t only rank the sites but also gives the information of that site related to SEO. That information consists of global rank, specific country rank, bounce rate, pageviews and visitors percentage, organic traffic percentage, keywords, backlinks and much more.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;13. CopyScape&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;This is also well known tool for webmaster by which we can check the plagiarism of any webpage. It is common rule in blogging that&amp;nbsp;we should not copy others content because it&#39;s illegal and has no benefit but if someone copies your content without permission then you can track your content violators through this tool. In simple words, we cancheck duplicate content&amp;nbsp;through this tool.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;14. Pingdom Website Loading Test&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://tools.pingdom.com/fpt/&quot; rel=&quot;nofollow&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Pingdom website loading test&lt;/a&gt;&amp;nbsp;is just alternative to Google PageSpeed Insights. We can also determine the loading speed or time through this tool. Pingdom website loading test allows us to check the loading speed from different countries of servers. After the process, it shows, how much did the webpage take to load, size of webpage and also gives&amp;nbsp;tips to improve the loading speed.&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;15. WordPress SEO By Yoast&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;This is the most popular WordPress SEO plugin which is being used by almost every WordPress user to SEO Optimize their websites and blogs. This plugin is free and is most recommended because it contains everything about SEO. It helps you to do on-page optimization like meta description, meta keywords, focus keywords, sitemaps and many more.&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;16. WooRank&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://www.woorank.com/&quot; rel=&quot;nofollow&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;WooRank&lt;/a&gt;&amp;nbsp;is another useful website review SEO tool which generates the SEO and other useful information about the given specific website. After generating review, it also gives the total score to that website by which we can know how much better we&#39;re going. The information is really brilliant which is being generated by this tool and we can easily know much about any particular website in a few clicks through this tool.&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;17. Drop My Link&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://dropmylink.com/&quot; rel=&quot;nofollow&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Drop My Link&lt;/a&gt;&amp;nbsp;is also a better tool for SEO Analyst which will help you to easily find such blogs on which you post comments and make backlinks through them. First you need to insert the keyword which can related to the top which you&#39;re linking back and choose the comment type blogs which can be CommentLuv blogs, dofollow comment blogs, .edu blogs and more. So,&amp;nbsp;&lt;a href=&quot;http://www.bloggeryard.com/2013/06/how-to-increase-backlinks-of-your-blog.html&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot;&gt;making backlinks&lt;/a&gt;&amp;nbsp;through this tool is easier.&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;18. MozBar&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;This is also useful tool for Bloggers which is basically plugin and extension for browsers. This bar allows you to get known about the Domain Authority, Page Authority, Page Rank, Alexa Rank, Indexed Pages and other related to SEO things. When you&#39;ll be surfing any webpage, this bar will provide you all the above data about that current webpage in ease. You can simply analyze SEO of other webpages.&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;19. Buffer&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Buffer is another most popular tool and application which be helpful for bloggers to drive more traffic. This is not mostly related to SEO but I would like to share them because this is awesome. This tool allows you to share the posts of your blog on different social networking sites with one click only. You can&amp;nbsp;&lt;a href=&quot;http://www.bloggeryard.com/2013/09/drive-social-media-traffic-towards-your-blog.html&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot;&gt;promote your blog on social networks&lt;/a&gt;while snoozing by scheduling posts. Simply, this tool helps you to socialize your content easily.&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;20. Craftkeys&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;Craftkeys is a useful tool for bloggers to analyze the competitor&#39;s keywords. By this tool, you can easily know that what keywords your competitor is trying to rank in Google and helps you to beat him/her. This tool gives you good information about keywords of the competitor just by giving domain, url or keyword.&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/5459693038966211597/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/top-seo-tolls-for-blogger-seo-tolls-for.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/5459693038966211597'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/5459693038966211597'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/top-seo-tolls-for-blogger-seo-tolls-for.html' title='Top Seo Tolls For Blogger | Seo Tolls for blogs '/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-6329950875533965709</id><published>2014-03-27T04:20:00.000-07:00</published><updated>2014-03-27T04:20:34.204-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Ahrefs"/><category scheme="http://www.blogger.com/atom/ns#" term="Backlink watch"/><category scheme="http://www.blogger.com/atom/ns#" term="Dofollow Backlink Checker"/><category scheme="http://www.blogger.com/atom/ns#" term="get high PR backlinks"/><category scheme="http://www.blogger.com/atom/ns#" term="how to increase backlinks"/><category scheme="http://www.blogger.com/atom/ns#" term="Link diagnosis"/><category scheme="http://www.blogger.com/atom/ns#" term="online back link checker"/><title type='text'>Top Back Link Checker Online Tools | Website  Back Link Checking Tool  </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
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&lt;b&gt;&lt;u&gt;&lt;span style=&quot;color: #cc0000;&quot;&gt;&lt;span style=&quot;font-family: arial, sans-serif; text-align: left; white-space: nowrap;&quot;&gt;Best Free&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: arial, sans-serif; text-align: left; white-space: nowrap;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: arial, sans-serif; text-align: left; white-space: nowrap;&quot;&gt;Online&lt;/span&gt;&lt;span style=&quot;background-color: white; font-family: arial, sans-serif; text-align: left; white-space: nowrap;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: arial, sans-serif; text-align: left; white-space: nowrap;&quot;&gt;Back link Checker Tools&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px; white-space: nowrap;&quot;&gt;Online Back link&amp;nbsp;checker&lt;/span&gt;&lt;span style=&quot;font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px; white-space: nowrap;&quot;&gt;&amp;nbsp;tool&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/u&gt;&lt;/b&gt;&lt;/h2&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #555555; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px; white-space: nowrap;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;background-color: white; color: #555555; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px;&quot;&gt;Being a blogger and webmaster, It&#39;s important to learn the basics of search engine optimization. We&#39;ve discussed many things about SEO for newbies and also for pros. If you&#39;re known a bit to SEO then you might have heard about backlinks. We&#39;ve also written several posts about backlinks which are&amp;nbsp;&lt;/span&gt;&lt;a href=&quot;http://www.bloggeryard.com/2013/06/how-to-increase-backlinks-of-your-blog.html&quot; style=&quot;background-color: white; color: #2aa4cf; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px; text-decoration: none;&quot;&gt;how to increase backlinks&lt;/a&gt;&lt;span style=&quot;background-color: white; color: #555555; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px;&quot;&gt;,&amp;nbsp;&lt;/span&gt;&lt;a href=&quot;http://www.bloggeryard.com/2013/06/what-are-dofollow-and-nofollow-links.html&quot; style=&quot;background-color: white; color: #2aa4cf; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px; text-decoration: none;&quot;&gt;nofollow and dofollow links&lt;/a&gt;&lt;span style=&quot;background-color: white; color: #555555; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px;&quot;&gt;,&amp;nbsp;&lt;/span&gt;&lt;a href=&quot;http://www.bloggeryard.com/2013/11/get-high-pr-backlinks.html&quot; style=&quot;background-color: white; color: #2aa4cf; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px; text-decoration: none;&quot;&gt;get high PR backlinks&lt;/a&gt;&lt;span style=&quot;background-color: white; color: #555555; font-family: Georgia, &#39;Times New Roman&#39;, serif; line-height: 24px;&quot;&gt;&amp;nbsp;and many more. Well, creating backlinks is just another thing which we should do regularly in order to good rank in SERP. But sometimes, we&#39;re interested to know that how much backlinks we&#39;ve made till now. There are many ways for this to check the backlinks of our blog but in this post, I&#39;m going to share some best backlink checker tools which will help you to analyze your backlinks easily.&lt;/span&gt;&lt;/div&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;div style=&quot;text-align: justify;&quot;&gt;
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&lt;a href=&quot;&quot; name=&quot;more&quot; style=&quot;background-color: white; color: #555555; line-height: 24px;&quot;&gt;&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
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&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;1. Ahrefs&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://ahrefs.com/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Ahrefs&lt;/a&gt;&amp;nbsp;has the largest index of live backlinks which are updated after every 15 minutes, it&#39;s quite simple to use for any beginner yet it provide deep enough statistics that are needed and trusted by gurus, it provide stats such as, inbound and internal backlinks, anchor text cloud, &amp;nbsp;incoming links TLD chart etc. Ahrefs have paid plans starting from 79$ monthly to 499$ monthly and free version of Ahrefs can allow you to see up to 10 backlinks per request (you can see the exact number but details will only be shown of 10 first backlinks).&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;2. Majestic SEO&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://www.majesticseo.com/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Majestic SEO&lt;/a&gt;&amp;nbsp;is one of the oldest backlink checker tool, although it can be a little hard for any newbie to get hang of it metric showing interface but once you do you won&#39;t regret it, it can show 90 days accurate backlink history of any domain and some usual basic features such as anchor text cloud, backlink attribute chart. MajesticSEO plans starts from 49.99$ monthly to whopping 1599.96$ monthly, although free version won&#39;t allow you to see detailed reports but still there&#39;s a lot you can do with it.&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;3. Open Site Explorer&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://opensiteexplorer.org/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Open Site Explorer&lt;/a&gt;&amp;nbsp;is owned by Moz (formally known as SEOMOZ ), it&#39;s one of the best new tool out there, it shows some of the newest metrics like domain authority and page authority, and the basic usual info as well, you can compare sites as well head to head. Open Site Explorer packages starts from 99$ per month to 599$ per month, and you can get free 30 days trial of its 99$ per month stand package without any commitment.&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;4. Backlink Watch&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://www.backlinkwatch.com/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Backlink watch&lt;/a&gt;&amp;nbsp;is a free backlink explorer which is powered by Ahrefs but the difference between it and ahrefs is that in backlinkwatch you can see every backlink linking to your domain without paying a dime although the report isn&#39;t as fancy as it&#39;s in Ahrefs but it&#39;s free and accurate.&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; color: #555555; line-height: 25px; margin-bottom: 10px; margin-top: 10px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif; font-size: small;&quot;&gt;5. Link Diagnosis&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #555555; line-height: 24px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Georgia, Times New Roman, serif;&quot;&gt;&lt;a href=&quot;http://www.linkdiagnosis.com/&quot; style=&quot;color: #2aa4cf; text-decoration: none;&quot; target=&quot;_blank&quot;&gt;Link diagnosis&lt;/a&gt;&amp;nbsp;is powered &amp;nbsp;by Iacquire, it&#39;s a free tool just like Backlinkwatch, there are several settings to play with before requesting report for your domain like you can change the engine, report type etc.&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
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&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/6329950875533965709/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/top-back-link-checker-online-tools.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/6329950875533965709'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/6329950875533965709'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/top-back-link-checker-online-tools.html' title='Top Back Link Checker Online Tools | Website  Back Link Checking Tool  '/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-3836132823505940429</id><published>2014-03-07T05:25:00.000-08:00</published><updated>2014-03-13T23:26:12.943-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="8051 projects using ldr"/><category scheme="http://www.blogger.com/atom/ns#" term="ldr light system"/><category scheme="http://www.blogger.com/atom/ns#" term="ldr sensor using micro controller"/><category scheme="http://www.blogger.com/atom/ns#" term="street light"/><category scheme="http://www.blogger.com/atom/ns#" term="street light circuit"/><category scheme="http://www.blogger.com/atom/ns#" term="street light using transistor"/><title type='text'>Automatic street Light system using microcontroller</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;h2 class=&quot;post-title entry-title&quot; style=&quot;color: blue; line-height: 20px; margin: 0px 0px 10px; padding: 0px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;
Automatic Street Light Control System.(Sensor using LDR &amp;amp; Transistor BC 547.) Very Simple.&lt;/span&gt;&lt;/h2&gt;
&lt;div class=&quot;post-header-line-1&quot;&gt;
&lt;/div&gt;
&lt;div class=&quot;post-body entry-content&quot; style=&quot;margin: 0px; padding: 0px 10px 0px 0px;&quot;&gt;
&lt;div style=&quot;line-height: 22px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;b&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large; line-height: 19.933334350585938px;&quot;&gt;Briefing:&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div style=&quot;line-height: 22px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;line-height: 22px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 21px; text-align: justify;&quot;&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;line-height: 26px;&quot;&gt;Her is our new simple Electrical/Electronics project about Automatic Street Light Control System.&lt;/span&gt;&lt;span style=&quot;line-height: 26px;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;ul style=&quot;line-height: 22px; margin: 0px 20px 20px 0px; padding-left: 40px;&quot;&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large; line-height: 26px;&quot;&gt;it&amp;nbsp;is a simple and powerful concept, which uses transistor (BC 547 NPN) as a switch to switch ON and OFF the street light system automatically.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;line-height: 19.933334350585938px;&quot;&gt;It automatically switches ON lights when the sunlight goes below the visible region of our eyes.&lt;/span&gt;&lt;span style=&quot;line-height: 26px;&quot;&gt;&amp;nbsp;(e.g in evening after Sunset).&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;line-height: 26px;&quot;&gt;it automatically switches OFF lights when Sunlight fall on it&amp;nbsp; ( i.e on LDR )&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;line-height: 26px;&quot;&gt;e.g in morning, by using a sensor called&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;line-height: 26px;&quot;&gt;LDR&amp;nbsp;(Light Dependent Resistor) which senses the light just like our eyes.&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;div style=&quot;line-height: 22px; text-align: justify;&quot;&gt;
&lt;b&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large; line-height: 19.933334350585938px;&quot;&gt;Advantages:&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;ul style=&quot;line-height: 22px; margin: 0px 20px 20px 0px; padding-left: 40px;&quot;&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large; line-height: 19.933334350585938px;&quot;&gt;By using this Automatic system for street light controlling, we can reduce energy consumption because the manually operated street lights are not switched off properly even the sunlight comes and also not switched on earlier before sunset.&amp;nbsp;&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;line-height: 19.933334350585938px;&quot;&gt;In sunny and rainy days, ON&amp;nbsp; and OFF time differ&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;line-height: 19.933334350585938px;&quot;&gt;&lt;span class=&quot;short_text&quot; id=&quot;result_box&quot; lang=&quot;en&quot;&gt;&lt;span class=&quot;hps alt-edited&quot;&gt;noticeably&lt;/span&gt;&lt;/span&gt;&amp;nbsp;which is one of the major disadvantage of using timer circuits or manual operation for switching the street light system.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;
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&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large; line-height: 19.933334350585938px;&quot;&gt;Enough....Now lets begin ( Step by Step)&lt;/span&gt;&lt;/div&gt;
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&lt;b&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Requirements&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
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&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;LDR Light Dependent Resistor&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Take 2 transistors. (NPN transistor- BC547 or BC147 or BC548)&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Resistor- 1K, 330Ohm, 470 ohm&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Light emitting diode (LED) - Any color&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connecting wires- Use single-core plastic-coated wire of 0.6mm diameter (the standard size)-You can use wire that is used for Computer&amp;nbsp;Networking.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Power supply-6V or 9V&lt;/span&gt;&lt;/li&gt;
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&lt;b&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Procedure&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
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&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Insert first transistor Q1-BC547 (NPN)&amp;nbsp;on breadboard (or general PCB) as shown in the circuit diagram 1.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connect&amp;nbsp;another transistor Q2- BC547 (NPN) on breadboard as in step 1.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connect&amp;nbsp; wires across emitter pin of both transistors and –ve terminal of battery (lowest/ bottom row&amp;nbsp;of breadboard.)&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connect&amp;nbsp;&amp;nbsp;a wire across Collector pin of transistor Q1 and Base pin of transistor Q2.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connect&amp;nbsp;a resistor 1K across positive terminal of battery (topmost row of breadboard) and Collector pin of transistor Q1.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connect&amp;nbsp;&amp;nbsp;Light Dependent Resistor (LDR) across positive terminal of battery (topmost row of breadboard) and base terminal of transistor Q1.&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;insert a resistor- 330 Ohm across base pin of transistor Q1 and negative terminal of battery (lowest bottom row of breadboard).&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;text-align: justify;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Connect a resistor 330R across&amp;nbsp;positive terminal of battery (topmost row of breadboard) and anode terminal of LED (Light emitting diode) &amp;amp; Connect the cathode terminal of LED to Collector pin of transistor Q2.&lt;/span&gt;&lt;/li&gt;
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&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;The simple circuit is ready for testing now. Connect 6V battery terminals to the circuit as show in&amp;nbsp;figand see the output. As you block light falling on&amp;nbsp;Light dependent resistor&amp;nbsp;(LDR), the LED glows.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;LED GLOWS EVEN IN LESS DARKNESS. Use torch light or Lighter&amp;nbsp;if the LED glows in less darkness. in addition, you can try to adjust the sensitivity of this&amp;nbsp;circuit by using a variable resistor in place of R1-300Ohm. Try this circuit with other resistances as well, (e.g, 1K&lt;span class=&quot;st&quot;&gt;Ω&lt;/span&gt;, 10K&lt;span class=&quot;st&quot;&gt;Ω&lt;/span&gt;&amp;nbsp;and 100K&lt;span class=&quot;st&quot;&gt;Ω&lt;/span&gt;, etc)&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;background-color: white;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;b&gt;Circu&lt;/b&gt;&lt;b&gt;it Diagram 1&lt;/b&gt;.Automatic Street Light Control System.(Sensor using LDR &amp;amp; Transistor BC 547.) Very Simple.&amp;nbsp; We have tried this one in this&amp;nbsp;tutorial&amp;nbsp;bu you can also try the second one&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large; line-height: 22px;&quot;&gt;&lt;b&gt;Circu&lt;/b&gt;&lt;b&gt;it Diagram 2&amp;nbsp;&lt;/b&gt;&lt;span style=&quot;background-color: white;&quot;&gt;.Automatic Street Light Control System.(Sensor using LDR &amp;amp; Transistor BC 547.) Very Simple.&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;i style=&quot;text-align: left;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;text-align: left;&quot;&gt;You can see now that we have blocked light falling on&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;text-align: left;&quot;&gt;Light dependent resistor&amp;nbsp;(LDR), so the LED glows&amp;nbsp;( LED = ON) &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/3836132823505940429/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/automatic-street-light-system-using.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/3836132823505940429'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/3836132823505940429'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/automatic-street-light-system-using.html' title='Automatic street Light system using microcontroller'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-8665055216794859568</id><published>2014-03-07T05:17:00.001-08:00</published><updated>2014-03-07T05:17:07.472-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="capacitor"/><category scheme="http://www.blogger.com/atom/ns#" term="capacitor calculation"/><category scheme="http://www.blogger.com/atom/ns#" term="formula for capacitance calculator"/><category scheme="http://www.blogger.com/atom/ns#" term="series capacitor calculator parallel"/><title type='text'>Capacitor In Series Calculation formula</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;b style=&quot;color: #3d6699; font-family: Verdana, sans-serif; font-size: x-large;&quot;&gt;Formula &amp;amp; Equations for This Calculator&lt;/b&gt;&lt;br /&gt;
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&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1tjVDs4SJAo6_dBxxqUbeavGVNtI1fcvbuP27iytkzYP6L38cAUknKXuddgfUUooWv1l7DM_C6lcFtxuKNMdi-1prHxpMUOQtNE-VW-6YtunBcMI9IZgyf5T1giT1oQx6p5FoOzoSk08/s1600/123.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;Capacitor In Series Calculation formula&quot; border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1tjVDs4SJAo6_dBxxqUbeavGVNtI1fcvbuP27iytkzYP6L38cAUknKXuddgfUUooWv1l7DM_C6lcFtxuKNMdi-1prHxpMUOQtNE-VW-6YtunBcMI9IZgyf5T1giT1oQx6p5FoOzoSk08/s1600/123.jpg&quot; title=&quot;Capacitor In Series Calculation formula&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
&lt;b style=&quot;color: #3d6699; font-family: Verdana, sans-serif; font-size: x-large;&quot;&gt;&lt;br /&gt;&lt;/b&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;Finding Total Series Capacitance (C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;T&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;) when C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;1&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; and C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;2&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; Given;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;1/C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; = 1/C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; + 1/C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; = C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;||C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; = C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; x C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2 &lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;/ (C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; + C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;)&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;Finding C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;1&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; when C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;T&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; and C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;2&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; Given;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; = C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; × C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; / (C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; – C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;)&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;Finding C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;2&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; when C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;T&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; and C&lt;/b&gt;&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;1&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt; Given;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;2&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; = C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1 &lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;× R&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T &lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt;/ (C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;color: black;&quot;&gt; – C&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;T&lt;/span&gt; &lt;span style=&quot;color: black;&quot;&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/8665055216794859568/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/capacitor-in-series-calculation-formula.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/8665055216794859568'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/8665055216794859568'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/03/capacitor-in-series-calculation-formula.html' title='Capacitor In Series Calculation formula'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1tjVDs4SJAo6_dBxxqUbeavGVNtI1fcvbuP27iytkzYP6L38cAUknKXuddgfUUooWv1l7DM_C6lcFtxuKNMdi-1prHxpMUOQtNE-VW-6YtunBcMI9IZgyf5T1giT1oQx6p5FoOzoSk08/s72-c/123.jpg" height="72" width="72"/><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-4883738167578212135</id><published>2014-01-26T05:32:00.001-08:00</published><updated>2014-01-26T05:32:25.113-08:00</updated><title type='text'>Maths problem on Mixtures and easy solutions</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;h3 class=&quot;post-title entry-title&quot; itemprop=&quot;name&quot;&gt;
Mixtures questions and its solutions &lt;/h3&gt;
&lt;div class=&quot;post-header&quot;&gt;

&lt;/div&gt;
This is the extension of Averages which we have discussed earlier. &lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;Formulae and shortcuts used to solve the following problems are discussed in the previous post.&lt;/span&gt;&lt;/div&gt;
&lt;br /&gt;
&lt;b&gt;Solved Problems&lt;/b&gt;&lt;br /&gt;
1. Let the cost of 2 quantities of rice be Rs.15 and Rs.19 per kg. Find the ratio of mixture which cost Rs.18 per kg?&lt;br /&gt;
Soln.:&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method1:&lt;/u&gt;&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the quantity of rice of quality A (Rs.15/kg) be &#39;x&#39; &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the quantity of rice of quality B (Rs.19/kg) be &#39;y&#39;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; As per the problem, 15x+19y = 18(x+y) &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; y = 3x =&amp;gt; x/y = 1/3&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.&lt;br /&gt;
&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method2:&lt;/u&gt; Using shortcut,&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;img alt=&quot;&quot; src=&quot;data:image/png;base64,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&quot; /&gt;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Therefore, ratio is 1:3 &lt;br /&gt;
&amp;nbsp; &lt;br /&gt;
2. Let the cost of 2 quantities of rice be Rs.15 (quality A) and Rs.19 
(quality B) per kg. Find the quantity of rice of quality A that has to 
be mixed with 27kg of quality B to make the cost of rice as Rs.18? &lt;br /&gt;
Soln.:&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method1:&lt;/u&gt;&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the quantity of rice of quality A (Rs.15/kg) be &#39;x&#39; &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the quantity of rice of quality B (Rs.19/kg) be &#39;y&#39;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; As per the problem, 15x+19y = 18(x+y) &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; y = 3x =&amp;gt; x/y = 1/3&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; =&amp;gt; 3 parts of quality B is to be mixed with 1 part of quality A&amp;nbsp; &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; 27kg of quality B is to be mixed with 9kg of quality A.&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Ans: 9kgs &lt;br /&gt;
&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method2:&lt;/u&gt; Using shortcut,&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;img alt=&quot;&quot; src=&quot;data:image/png;base64,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&quot; /&gt;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Therefore, ratio is 1:3 &lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp; =&amp;gt; 3 parts of quality B is to be mixed with 1 part of quality A&amp;nbsp; &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; 27kg of quality B is to be mixed with 9kg of quality A.&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Ans: 9kgs&lt;br /&gt;
&lt;br /&gt;
3. Let the cost of 2 quantities of rice be Rs.15 and Rs.19 per kg. These
 2 qualities of rice are mixed and sold at Rs.27 per kg of profit 50%. 
Find the ratio in which 2 qualities of rice mixed?&lt;br /&gt;
Soln.:&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method1:&lt;/u&gt;&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the quantity of rice of quality A (Rs.15/kg) be &#39;x&#39; &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the quantity of rice of quality B (Rs.19/kg) be &#39;y&#39;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Given Selling price, SP = 27 and the profit % is 50%&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; We know that the profit%, p% = (SP-CP)/CP * 100&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; =&amp;gt; 50/100 = (27 - CP)/CP &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; CP = 18&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; As per the problem, 15x+19y = 18(x+y) &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; y = 3x =&amp;gt; x/y = 1/3&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.&lt;br /&gt;
&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method2:&lt;/u&gt; Using shortcut,&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Given Selling price, SP = 27 and the profit % is 50%&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; We know that the profit%, p% = (SP-CP)/CP * 100&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; =&amp;gt; 50/100 = (27 - CP)/CP &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; CP = 18&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;img alt=&quot;&quot; src=&quot;data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAACaCAIAAABdWf97AAAERklEQVR4nO2dy47rIBBE8/8/3VkgWZbtEEwDXU3VWdxF5EdRJx4zmZj7McHKJzqACEPueZF7XuSeF7nnRe55kXte5J4XuedF7nmRe17knhe550XueZF7XuSeF7nnRe55kXte4t1/Pp/y75noUJEcw5/dRnzLh/voICjcC5lUTnDjx/ta7guPhezp3nTd35B7Xhjda6JXoHNff4WK+zxf7llYVkh8y3J/gc79gttbFuju93J/QOfe5n+EmQWiz3RFFHLPi9zzIve8pHFPNQdcM9hMhZLoXzbMZG1ur3/lAPNVubH+xUNL2eOW+tcPKmuJm+kPGU7iBrfRHzWQ3PVtoD9wCOouktjwiYs7SKo/PHbK1u6E9/gWhMDxCUaB0GYjIFEhQowCpNM6OCFRcowCp9lHoOIBRRkFVL9n0IJhpRkFWsuGGSk6wCyguoYKc4CYaRQgjYPEuAMaaxThvYcHqICbbBSRH5gDizcG9xb1F1Js8Ubi3tZ/JQZevPG4t5Xfgcwg3qjc2xIrWcQbm3ub7CaReCN0b/MeaU4l3jjd2wRP6cQbrXsbaiujeGN2b4OcJRVv5O7NbS6veJN7c/hLLd7knhm550XueZF7XuSeF7nnRe6v8Kzzue3AuuFZ33fPUXVzXOhyz4jc83K+39u+4k3u7zBc8YWdx9aHrntedL/nRe55kXte5J4XfaZLxMZ265AO+4BWvJG7ZxZvzO7JxRutez2TZZzu9SxmIVlcP3oG+yBTVj9ae+FMmqB+tObKhRwp/WitpTsJIvrRGmuPoOfzo7UVfwEdzk94++EBKuAm8wPSO0iMO6Cx/EA1DhXmADGTH8CuESNFBxgPYMsFtGBYafyg9XsBKh5QFD9Qzf4CJyRKDj84nf4FJCpECD8gbbaDEDg+gR+EHjsIj52ytTPhDXqIDZ+4OIvubgiRf26IOrGfDcQXogaStb5txBdi/sq8/pR+NhNfWD+ofCVuKb6w+stFK0/mZ2PxhZUDzFTl9uIL675TuuY0fkjEF9YMNkehVOILKx4lmH0CP4TiC7MHjl4rrfjC3CfI5h3aD7n4wrwScMuV+NmA9ivxC0CsWOLXoJZ5kXte5J4XuedF7nmR++m0L9B7LON8pn5kz4q/cj+d9oW5X/1PHf6VvuV+Lsd1+VfV45b1I9cP+P8IHfuIV2x43b+9jbVsedl+D87Dt+roXrm/H/91sL7dzPd2/juF6U4FyNuBP070fk0APV31vmV8t7H6e39X943Xff2Vlr1ag/XtZrrum6kM/3Id97lv3+y6V8c+5/O1u3/cpb79HnQUdX/l/jM/fq73dkiXbR5vY+Tu22+OLZvVgnXscznf4xzk15am634n9/dXHq9j8vu9zflluGWzn7v37WZvJiYtk52Nf+bDonk+L3LPy8i5nn/Ly/ZiKmqZF7nnRe55kXte5J4XuedF7nmRe17knhe55+ULNgqL0eabXMIAAAAASUVORK5CYII=&quot; /&gt;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Therefore, the ratio of quantities mixed to make the quality of Rs.18 is 1:3.&lt;br /&gt;
&lt;br /&gt;
4. A man purchased TV and Washing machine for Rs.30000. He sold the TV 
at 30% profit and washing machine at 60% profit. He makes overall profit
 of 50%. Then find for how much did he purchased TV and washing machine?&lt;br /&gt;
Soln:&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method1:&lt;/u&gt;&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the cost price of TV be &#39;x&#39; &lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Let the cost price of washing machine be &#39;y&#39;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; As per the problem,&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; x + y = 30000 ------&amp;gt; Eq. 1&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; SP of TV = 1.3x&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; SP of washing machine = 1.6y&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.3x + 1.6y = 30000 * 1.5&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.3x + 1.6y = 45000 --------&amp;gt; Eq. 2&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; On solving equations 1 and 2, x = 10000 and y = 20000&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Therefore, cost price of TV and washing machine are Rs.10000 and Rs.20000 respectively.&lt;br /&gt;
&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;u&gt;Method2:&lt;/u&gt; Using shortcut,&lt;br /&gt;
&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;img alt=&quot;&quot; src=&quot;data:image/png;base64,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&quot; /&gt;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Therefore, ratio is 1:2. 3 parts is equivalent to 30000&lt;br /&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; Cost of TV is 10000 (1 part) and Cost of washing machine is 20000 (2 parts)&lt;i&gt;&lt;/i&gt;&lt;/div&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/4883738167578212135/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/maths-problem-on-mixtures-and-easy.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/4883738167578212135'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/4883738167578212135'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/maths-problem-on-mixtures-and-easy.html' title='Maths problem on Mixtures and easy solutions'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-5834092494441861638</id><published>2014-01-26T05:30:00.000-08:00</published><updated>2014-01-26T05:30:01.919-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="average problems"/><category scheme="http://www.blogger.com/atom/ns#" term="average questions"/><category scheme="http://www.blogger.com/atom/ns#" term="Averages and Mixtures problems"/><category scheme="http://www.blogger.com/atom/ns#" term="Averages problems"/><title type='text'>Averages and Mixtures problems | Formulae Shortcuts  questions</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot;&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt;&quot;&gt;
&lt;h2 class=&quot;r&quot; style=&quot;text-align: left;&quot;&gt;
&lt;em&gt;Mixture&lt;/em&gt; and Alligation &lt;em&gt;Shortcut&lt;/em&gt; Methods&lt;/h2&gt;
&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: inherit;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt;&quot;&gt;
&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: inherit;&quot;&gt;Formulae:&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto; mso-list: l1 level1 lfo1; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;1.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Average = sum of quantities/number of quantities&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto; mso-list: l1 level1 lfo1; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;2.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Sum = avg * no. of quantities&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto; mso-list: l1 level1 lfo1; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;3.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;If the numbers are in A.P. (Arithmetic Progression), then the avg of numbers is given by&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;Avg = sum/n =[ (n/2)(a+l)]/n&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;= (a+l)/2&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;Where&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp; &lt;/span&gt;n – no. of quantities&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;a – first term or value&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;l – last term or value&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto; mso-list: l1 level1 lfo1; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;4.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Weighted Average:&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;Section1:&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;No. of quantities: m&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Avg of section1: p&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;Section2:&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;No. of quantities: n&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-tab-count: 1;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Avg of section1: q&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;Avg of section1 and section2 = (m*p + n*q)/(m +n)&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0in 0in 0pt;&quot;&gt;
&lt;b style=&quot;mso-bidi-font-weight: normal;&quot;&gt;&lt;span style=&quot;font-family: inherit;&quot;&gt;Points to remember/Shortcuts&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;1.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Average lies between minimum and maximum values.&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level2 lfo2; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;a.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Avg &amp;gt; minimum value&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level2 lfo2; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;b.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Avg &amp;lt; maximum value&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;margin: 0in 0in 0pt 0.5in; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;font-family: inherit;&quot;&gt;&lt;span style=&quot;mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;2.&lt;span style=&quot;font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;If every quantity is increased/decreased by ‘k’ value, then the avg also get increased/decreased by the same ‘k’ value.&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;i&gt;&lt;/i&gt;&lt;/div&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/5834092494441861638/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/averages-and-mixtures-problems-formulae.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/5834092494441861638'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/5834092494441861638'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/averages-and-mixtures-problems-formulae.html' title='Averages and Mixtures problems | Formulae Shortcuts  questions'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-3679991144501679433</id><published>2014-01-26T05:27:00.004-08:00</published><updated>2014-01-26T05:27:36.605-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="questions for time and work"/><category scheme="http://www.blogger.com/atom/ns#" term="questions on time and work"/><title type='text'>time and work questions solutions </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;h2 style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #cc0000;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;i&gt;Time and work questions solutions&amp;nbsp;&lt;/i&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
&lt;h2 style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;i&gt;&lt;b&gt;Difficulty Level - Medium&lt;/b&gt;&lt;br /&gt;


&lt;/i&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 1.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A
can work on 1km railway track in 1 day. In how many days, will he able to &lt;i&gt;&lt;b&gt;complete&lt;/b&gt;&lt;/i&gt; the work on 12km railway track?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln: no. of days = total
work / work done in 1 day&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify; text-indent: 0.5in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Therefore,
no. of days taken = 12/1 = 12 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify; text-indent: 0.5in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify; text-indent: 0.5in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 2.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A
can complete the work in 15 days. What fraction of work will be completed in 1
day?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln.: &lt;span&gt;&amp;nbsp; &lt;/span&gt;Let the total work is 1 unit.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Work in 1day = total
work/no. of days to complete&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;= 1/15&lt;sup&gt;th&lt;/sup&gt; of work&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;


&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 3.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A
can do a piece of work in 3 days and B can do a piece of work in 5 days. In how
many days will the work be completed if both A and B work together?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln.: &lt;b&gt;Using formula:&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Work
done by A in 1 day = 1/3&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Work done by B in 1 day = 1/5&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Total work done by A and B in
1 day = 1/3 + 1/5 = 8/15&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, no. of days to
complete work by A and B together = 1/(Total work) = 1/(8/15) = 15/8 days which
is less than 3 and 5&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp; &lt;/span&gt;Using
shortcut/analysis/assumption&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Let
us consider the total work be 15 units (LCM of 3 and 5)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;So work done by A in 1 day =
15/3 = 5 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Similarly work done by B in 1
day = 15/5 = 3 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;So total work done by A and B
in 1 day = 5 + 3 = 8 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, no. of days to
complete total work i.e. 15 units = total work/work done in 1 day = 15/8 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Note:&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;a.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Work
done by A and B in 1 day &lt;b&gt;will always be
greater than &lt;/b&gt;that of A and B individually&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;b. No. of days taken by A and B together &lt;b&gt;will always be less than&lt;/b&gt; that of A and B
individually&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;


&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 4.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A
can do a piece of work in 6 days, B can do a piece of work in 4 days and C can
do a piece of work in 12 days. Find the no. of days to complete the work if A,
B and C work together?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln.: &lt;b&gt;Using formula:&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Work
done by A in 1 day = 1/6&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Work done by B in 1 day = ¼&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Work done by C in 1 day = 1/12&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Total work done by A, B and C
in 1 day = 1/6 + ¼ + 1/12 = 12/24 = 1/2&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, no. of days to
complete work by A, B and C together = 1/(Total work) = 1/(1/2) = 2 days which
is less than 4, 6, 12&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Using
shortcut/analysis/assumption&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Let
us consider the total work be 24 units (LCM of 4, 6, 12)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;So work done by A in 1 day =
24/4 = 6 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;work done by B in 1 day = 24/6
= 4 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;work done by C in 1 day =
24/12 = 2 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;So total work done by A, B and
C in 1 day = 6 + 4 + 2 = 12 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, no. of days to
complete total work i.e. 24 units = total work/work done in 1 day = 24/12 = 2
days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;The above Note is
valid here as well.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 5.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A
can do a piece of work in 6 days and B can do a piece of work in 12. Find the
no. of days to complete the work if A and B work alternatively?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln.: &lt;b&gt;Using formula:&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Work
done by A in 1 day = 1/6&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Work done by B in 1 day = 1/12&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Total work done by A and B
working 1 day each = 1/6 + 1/12 = 3/12 = ¼&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, 1/4&lt;sup&gt;th&lt;/sup&gt; of
work is done in 2days.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;No. of days to complete total
work if A and B work alternatively = 1/((1/4)/2) = 8 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Using
shortcut/analysis/assumption&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Let
us consider the total work as 12 units (LCM of 6, 12)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;So work done by A in 1 day =
12/6 = 2 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;work done by B in 1 day =
12/12 = 1 unit&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Total work done by A and B
working 1 day each = 2 + 1 = 3 units in 2 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, work done in 1 day
= work/no. of days = 3/2 units&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;No.
of days to complete work = total work/work in 1 day = 12/(3/2) = 8 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;


&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 6.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;30
men can complete a job in 40 days. Then 25 men can complete the same job in how
many days?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln.: As per M1D1 =
M2D2&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp; &amp;nbsp; &lt;/span&gt;30
* 40 = 25 * x&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;=&amp;gt; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;x
= 30 * 40/25 = 48 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 7.&amp;nbsp;&lt;span&gt;&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;30
men can complete 1500 units in 24 days working 6hrs a day. In how many days can
18 men can complete 1800 units working 8 hrs a day?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;


&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Soln.: As per the &lt;a href=&quot;http://mathswinner.blogspot.in/2012/06/time-and-work-formula-shortcuts.html&quot;&gt;formula&lt;/a&gt;&amp;nbsp; (from my earlier blog), M1D1h1/W1 = M2D2h2/W2&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; 30*24*6/1500 = 18*x*8/1800&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; =&amp;gt; x = 36 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;


&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 8.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A and B can do a work in 10 and 15
days respectively. Then combinedly A &amp;amp; B, in how many days the work will be
completed?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Soln.: As per the &lt;a href=&quot;http://mathswinner.blogspot.in/2012/06/time-and-work-formula-shortcuts.html&quot;&gt;formula&lt;/a&gt;&amp;nbsp; (from my earlier blog), x*y/(x + y)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A
and B together can complete the work in 10 * 15/(10 + 15) = 6 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 9.&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A can do a work in 10 and, A and B
together can do a work in 6 days. In how many days B can complete the same
work?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Soln.: As per the &lt;a href=&quot;http://mathswinner.blogspot.in/2012/06/time-and-work-formula-shortcuts.html&quot;&gt;formula&lt;/a&gt;&amp;nbsp; (from my earlier blog), x*y/(x - y)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp; B alone
can complete the work in 10 * 6/(10 - 6) = 15 days&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 10.&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;A is twice faster than B and B can
complete in 12 days alone. Find the number of days to complete if A and B
together work?&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Soln.: &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Given B works in 12 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;A is twice faster
than B =&amp;gt; A takes 2 times less time than B &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-left: 0.25in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;Therefore, A
completes work in 12/2 = 6 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;
&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;A
and B together can complete in 12 * 6/(12 + 6) = 4 days&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;h2 style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;i&gt;&amp;nbsp;&lt;/i&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
&lt;/div&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/3679991144501679433/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/time-and-work-questions-solutions.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/3679991144501679433'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/3679991144501679433'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/time-and-work-questions-solutions.html' title='time and work questions solutions '/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-1333421459777608559</id><published>2014-01-26T05:24:00.000-08:00</published><updated>2014-01-26T05:24:51.621-08:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="short tricks for time and work questions"/><category scheme="http://www.blogger.com/atom/ns#" term="time and work"/><category scheme="http://www.blogger.com/atom/ns#" term="time and work questions"/><title type='text'>Time And Work questions formula for placement</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;h2 class=&quot;post-title entry-title&quot; itemprop=&quot;name&quot; style=&quot;text-align: left;&quot;&gt;
Time And Work questions formula for placement&lt;/h2&gt;
&lt;div class=&quot;post-header&quot;&gt;
&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;&lt;b&gt;1&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
&lt;/span&gt;&lt;/span&gt;&lt;b&gt;&lt;i&gt;&lt;span lang=&quot;EN-IN&quot;&gt;Work
from Days:&lt;/span&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;table border=&quot;0&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoNormalTable&quot; style=&quot;margin-left: 0px; margin-right: 0px; text-align: left;&quot;&gt;
 &lt;tbody&gt;
&lt;tr&gt;
  &lt;td rowspan=&quot;2&quot; style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;If
  A can do a piece of work in &lt;i&gt;n&lt;/i&gt; days, then A&#39;s 1 day&#39;s work =&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
  &lt;td style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;&amp;nbsp; 1&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
  &lt;td rowspan=&quot;2&quot; style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
 &lt;/tr&gt;
&lt;tr&gt;
  &lt;td style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-IN&quot;&gt;n&lt;/span&gt;&lt;/i&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
 &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;&lt;b&gt;2&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;b&gt;
&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;b&gt;&lt;i&gt;&lt;span lang=&quot;EN-IN&quot;&gt;Days
from Work:&lt;/span&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;table border=&quot;0&quot; cellpadding=&quot;0&quot; cellspacing=&quot;0&quot; class=&quot;MsoNormalTable&quot; style=&quot;margin-left: 0px; margin-right: 0px; text-align: left;&quot;&gt;
 &lt;tbody&gt;
&lt;tr&gt;
  &lt;td rowspan=&quot;2&quot; style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;If
  A&#39;s 1 day&#39;s work =&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
  &lt;td style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;1&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
  &lt;td rowspan=&quot;2&quot; style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;,&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
  &lt;td rowspan=&quot;2&quot; style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;then
  A can finish the work in &lt;i&gt;n&lt;/i&gt; days.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
 &lt;/tr&gt;
&lt;tr&gt;
  &lt;td style=&quot;padding: 0in;&quot;&gt;&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-bottom: 0in; text-align: center;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;i&gt;&lt;span lang=&quot;EN-IN&quot;&gt;n&lt;/span&gt;&lt;/i&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/td&gt;
 &lt;/tr&gt;
&lt;/tbody&gt;&lt;/table&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;&lt;b&gt;3&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;b&gt;&amp;nbsp;
&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;b&gt;&lt;i&gt;&lt;span lang=&quot;EN-IN&quot;&gt;Ratio:&lt;/span&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 0.5in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;If
A is thrice as good a workman as B, then:&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 0.5in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;Ratio
of work done by A and B = 3 : 1.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 0.5in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot;&gt;Ratio
of times taken by A and B to finish a work = 1 : 3.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: normal; margin-left: 0.5in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;4.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;No. of days = total work / work done
in 1 day&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;5&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Relationship
between Men and Work&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;More men&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp; ------- can
do -------&amp;gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; More work&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Less men&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;------- can
do -------&amp;gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Less work&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;6&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Relationship
between Work and Time&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;More work&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp; -------- takes------&amp;gt; &amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
More Time&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Less work&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;-------- takes------&amp;gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
Less Time&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;7&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;b&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Relationship
between Men and Time&lt;/span&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;More men&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;------- can
do in -------&amp;gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Less Time&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;Less men&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;------- can
do in -------&amp;gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; More Time&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;8&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;If
M&lt;sub&gt;1 &lt;/sub&gt;persons can do W&lt;sub&gt;1&lt;/sub&gt; work in D&lt;sub&gt;1&lt;/sub&gt; days and M&lt;sub&gt;2&lt;/sub&gt;
persons can do W&lt;sub&gt;2&lt;/sub&gt; work in D&lt;sub&gt;2&lt;/sub&gt; days, then&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;b&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRYyyJAcyKifhYgCd30dcdujIgyE-a-5z2kwkCerQKjY3LfuvQm8TkAzAwIUH9vKgRdJD4PzOnMzPys0IDy5BB_Uh04RLMM061LYsvjN3XHGSCJr73WoUz1YhfjQEO0Nb5zPcQ-v7kU44/s1600/time_work_1.jpg&quot; /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;9&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;If
M&lt;sub&gt;1 &lt;/sub&gt;persons can do W&lt;sub&gt;1&lt;/sub&gt; work in D&lt;sub&gt;1&lt;/sub&gt; days for h&lt;sub&gt;1&lt;/sub&gt;
hours and M&lt;sub&gt;2&lt;/sub&gt; persons can do W&lt;sub&gt;2&lt;/sub&gt; work in D&lt;sub&gt;2&lt;/sub&gt; days
for h&lt;sub&gt;2&lt;/sub&gt; hours, then&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;b&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitaBvLgC5jNF0_SmthUwpD_v7uDDLZ2OwnZW8Gu4bWXGb3pRGKBXpUUv62syE2dSriYXGQASBXOBDQZsAgwtHyBkqIXWYK0TyLgZR1FcJ3Ktbiji6bzbT9hCUEca32Yhfik5R3CwGqa30/s1600/time_work_2.jpg&quot; /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&amp;nbsp;&lt;b&gt;Note&lt;/b&gt;:&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;If
works are same, then M1D1h1 = M2D2h2&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 1in; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;10&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;If
A can do a work in ‘x’ days and B can do the same work in ‘y’ days, then the
number of days required to complete the work if A and B work together is&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWb_qJKqP5D4q4064ZqLTRPoRQr3Lhj750yvdhoSWthPBqqzY4VPpz9aZKXeyAX0Uo7yHrgNDNeeoMKw83q-lq_Omu4kwPn7ggLnsFespNjeI_W4fMh9RIGvGrgysz51nhqYSYeBURrxs/s1600/time_work_3.jpg&quot; /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br clear=&quot;ALL&quot; /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;margin-left: 32.2pt; text-align: justify; text-indent: -0.25in;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;&lt;b&gt;11&lt;/b&gt;.&lt;span style=&quot;-moz-font-feature-settings: normal; -moz-font-language-override: normal; font-size-adjust: none; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-IN&quot; style=&quot;line-height: 115%;&quot;&gt;If
A can do a work in ‘x’ days and A + B can do the same work in ‘y’ days, then
the number of days required to complete the work if B works alone is&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #351c75;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;font-family: Verdana,sans-serif;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbugQXO3vrNH2HdVDFsV7i8_kbcWG0KjtavBv4MTCYG7a2JrP-nic88tuoiNj2X47yTLcIz7tuUCYfPdTisjMysFyhfbG-pLpCmdYZ7QbNeW1Sn_EQnKKr7a8Yg9mEJhhhTESkYmGFfUU/s1600/time_work_4.jpg&quot; /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/1333421459777608559/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/time-and-work-questions-formula-for.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/1333421459777608559'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/1333421459777608559'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2014/01/time-and-work-questions-formula-for.html' title='Time And Work questions formula for placement'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRYyyJAcyKifhYgCd30dcdujIgyE-a-5z2kwkCerQKjY3LfuvQm8TkAzAwIUH9vKgRdJD4PzOnMzPys0IDy5BB_Uh04RLMM061LYsvjN3XHGSCJr73WoUz1YhfjQEO0Nb5zPcQ-v7kU44/s72-c/time_work_1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-7839069301573271129</id><published>2013-09-24T08:27:00.000-07:00</published><updated>2014-03-13T23:27:30.308-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="how to get high ranking in google"/><category scheme="http://www.blogger.com/atom/ns#" term="how to use blogger"/><category scheme="http://www.blogger.com/atom/ns#" term="Robots Header Tags in blogger"/><category scheme="http://www.blogger.com/atom/ns#" term="Robots.txt Settings for Blogger"/><category scheme="http://www.blogger.com/atom/ns#" term="search engine optimization"/><category scheme="http://www.blogger.com/atom/ns#" term="seo for blogger"/><category scheme="http://www.blogger.com/atom/ns#" term="seo friendly website"/><category scheme="http://www.blogger.com/atom/ns#" term="Sitemap"/><title type='text'>HOW TO MAKE SEO FRIENDLY BLOGGER | SEO TIPS FOR MAKING SITE SEO FREE</title><content type='html'>&lt;script&gt;
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&lt;u&gt;BLOGGER SEO TIPS AND TRICKS &amp;nbsp;BLOGGER | BEST WAY FOR MAKING BLOGGER SEO FRIENDLY&lt;/u&gt;&lt;/h2&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;As we know about blogger is group of google and very good for posting articles and posting knowledgeable posts.You &amp;nbsp;should know about how to use blogger or other blogger type websites for posting articles or getting high ranking in google search results.If you understand what to do for getting high ranking in google or other search engines then it will be benefit for your websites. Okay lets start about seo.&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;color: #bf9000; font-size: large;&quot;&gt;Let&#39;s We Start Seo for Blogger&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;Step :- A&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;br /&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&amp;nbsp;Select all the key words which are&amp;nbsp;useful &amp;nbsp;for your website and describes all about your page.Be careful&amp;nbsp;&amp;nbsp;to select keywords, you can use google key word toll for making good key word or we can say hot key word for your page.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;Step :- B&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;After the making list of hot key words , you need to place these hot key words in your post for this you should use key word density tool to check key word density in your post. If the key word density&amp;nbsp;crosses&amp;nbsp;a limit then it gives bad impact in search results.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;Step :- C&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijLWlXV4-9DwdAm0DPz7_lsyIbJbF99wIlqlsJd_cVwWfACMivZWgqz-3dN17zY0hqEjaZziAzRRoF3AaqsF0aY_JUcSJcg5yu_YubjimYoMRMslsdyyhXP0xpCI5JjVM1F_TsRlqDFBM/s1600/yg55.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;SEO TIPS AND TRICKS&quot; border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijLWlXV4-9DwdAm0DPz7_lsyIbJbF99wIlqlsJd_cVwWfACMivZWgqz-3dN17zY0hqEjaZziAzRRoF3AaqsF0aY_JUcSJcg5yu_YubjimYoMRMslsdyyhXP0xpCI5JjVM1F_TsRlqDFBM/s640/yg55.jpg&quot; height=&quot;234&quot; title=&quot;SEO TIPS AND TRICKS&quot; width=&quot;640&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;In this picture some area is highlighted with red color, very important when you are going to post in blogger .&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;Now i am telling you about all so be careful when u read these steps&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;Step :- D&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;Post Title&lt;/b&gt;&lt;/span&gt;&lt;/h3&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh15mSkN6r5uoqUBPcHlBPhGWq5BIFo7jVBlifWZoPq4dsnmj0evtx4ClmG0VdCY0YoRb5eVuc05pYx78ZI2jcetmQiTn_F7p8BbGNMpNGn26G6U316SLw7OYTujZ-otdthJtH8cSRBbJw/s1600/yg55.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;Post Title in blogger&quot; border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh15mSkN6r5uoqUBPcHlBPhGWq5BIFo7jVBlifWZoPq4dsnmj0evtx4ClmG0VdCY0YoRb5eVuc05pYx78ZI2jcetmQiTn_F7p8BbGNMpNGn26G6U316SLw7OYTujZ-otdthJtH8cSRBbJw/s640/yg55.jpg&quot; height=&quot;146&quot; title=&quot;Post Title&quot; width=&quot;640&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;This one is the very most important section of blogger. When you are going to search any thing then search engines firstly read the post title of the page if post title matches with the search then it shows your page at first link. So it is very important to select the post title for this purpose you can use google search results more the search number more the&amp;nbsp;competition , so always try to chose post title which has law search numbers in google.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;Permalink in blogger&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;Permalink in blogger is also very very important for best seo friendly websites. So you have to chose custom permalink in blogger. It reflects your page with your post title so this good for google search result and getting top rank in search engine as well as affects the ranking factor.&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;Labels in blogger&amp;nbsp;&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;Labels are also most important to make seo friendly site and to get more traffic. Always try to select labels which are related to your post. If you are using labels but they are not using in your post then it gives negative&amp;nbsp;feedback to google search engine.So always select labels which has low&amp;nbsp;competition in google search&amp;nbsp;result.&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; After this i will tell you one more thing that is related to labels and have very big roll in making seo friendly websites and to give higher traffic.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;Location in blogger&amp;nbsp;&lt;/span&gt;&lt;/h3&gt;
&lt;div&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;According to new updates in google search engine&amp;nbsp;algorithms, locations is to be set when you are going to post. When you set location in google blogger then it gives an&amp;nbsp;opportunity to your page to be show by google in google events. When you set location in post&amp;nbsp;article then it gives a positive feedback to google search results, and show your page in top result in google.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;Step :- F&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;After the step D , you have to make some changes in your html&amp;nbsp;coding, Its not a big &amp;nbsp;task you have to follow some steps and in your blogger.&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u style=&quot;background-color: yellow;&quot;&gt;blogger title optimization for seo friendly site &amp;nbsp;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/h3&gt;
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&lt;br /&gt;&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;Follow these steps :-&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;ol style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin: 12px 0px; padding: 0px 0px 0px 30px; text-align: justify;&quot;&gt;
&lt;li style=&quot;line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Blogger &amp;gt; Template &amp;gt; Edit HTML&lt;/li&gt;
&lt;li style=&quot;line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Search for the below code in the &amp;lt;head&amp;gt; section of your template&lt;br style=&quot;margin: 0px; padding: 0px;&quot; /&gt;&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; background-repeat: no-repeat no-repeat; color: #333333; margin: 1em; padding: 1px 10px;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&amp;lt;title&amp;gt;&amp;lt;data:blog.pageTitle/&amp;gt;&amp;lt;/title&amp;gt;&lt;/div&gt;
&lt;/blockquote&gt;
&lt;/li&gt;
&lt;li style=&quot;line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Replace it with the below code&lt;br style=&quot;margin: 0px; padding: 0px;&quot; /&gt;&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; background-repeat: no-repeat no-repeat; color: #333333; margin: 1em; padding: 1px 10px;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&amp;lt;b:if cond=’data:blog.pageType == &amp;amp;quot;item&amp;amp;quot;’&amp;gt;&lt;br /&gt;
&amp;lt;title&amp;gt;&amp;lt;data:blog.pageName/&amp;gt; | &amp;lt;data:blog.title/&amp;gt;&amp;lt;/title&amp;gt;&lt;br /&gt;
&amp;lt;b:else/&amp;gt;&lt;br /&gt;
&amp;lt;title&amp;gt;&amp;lt;data:blog.pageTitle/&amp;gt;&amp;lt;/title&amp;gt;&lt;br /&gt;
&amp;lt;/b:if&amp;gt;&lt;/div&gt;
&lt;/blockquote&gt;
&lt;br /&gt;
&lt;/li&gt;
&lt;li style=&quot;line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Now, save your template.&lt;/li&gt;
&lt;/ol&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #666666; font-family: Lucida Sans Unicode, Verdana, Arial, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 14px; line-height: 21px;&quot;&gt;Note :- After making your site seo friendly these, &amp;nbsp;take back up for all html code.&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #666666; font-family: Lucida Sans Unicode, Verdana, Arial, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 14px; line-height: 21px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;h3 style=&quot;background-color: white; border-bottom-color: rgb(229, 229, 229); border-bottom-style: solid; border-bottom-width: 1px; color: #111111; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 15px; letter-spacing: -1px; line-height: 18px; margin: 12px 0px 10px; padding: 10px 0px;&quot;&gt;
Search Engine Optimization In &amp;nbsp;Your Post Title Heading&amp;nbsp;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
IN google these kind of settings &amp;nbsp;are &amp;nbsp;predefined but you have to change for getting more traffic or making seo friendly blog. Blogger &amp;nbsp;use H1 for homepage title, H2 for blog description and H3 to post titles. Due to the fact that the post titles are the second most important part of your blog after the main title, you should assign them an H2 instead of H3. By changing this your post title is optimize for getting higher result .&lt;/div&gt;
&lt;ol style=&quot;background-color: white; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin: 12px 0px; padding: 0px 0px 0px 30px;&quot;&gt;
&lt;li style=&quot;color: #666666; line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Go to Template &amp;nbsp;then &amp;nbsp;Edit HTML&lt;/li&gt;
&lt;li style=&quot;color: #666666; line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Search for (Press Ctrl + F) then search &lt;b&gt;.post&lt;/b&gt; h3 and replace all the occurrences of it with .post h2.&lt;/li&gt;
&lt;li style=&quot;line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;&lt;span style=&quot;color: #666666;&quot;&gt;Next search for,&lt;/span&gt;&lt;br style=&quot;margin: 0px; padding: 0px;&quot; /&gt;&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; margin: 1em; padding: 1px 10px;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&lt;span style=&quot;color: blue;&quot;&gt;&amp;lt;h3&amp;gt;&amp;lt;data:title/&amp;gt;&amp;lt;/h3&amp;gt;&lt;/span&gt;&lt;/div&gt;
&lt;/blockquote&gt;
&lt;/li&gt;
&lt;li style=&quot;line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;&lt;span style=&quot;color: #666666;&quot;&gt;Replace it with the below code that is bellow&amp;nbsp;&lt;/span&gt;&lt;br style=&quot;margin: 0px; padding: 0px;&quot; /&gt;&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; margin: 1em; padding: 1px 10px;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&lt;span style=&quot;color: blue;&quot;&gt;&amp;lt;h2&amp;gt;&amp;lt;data:title/&amp;gt;&amp;lt;/h2&amp;gt;&lt;/span&gt;&lt;/div&gt;
&lt;/blockquote&gt;
&lt;/li&gt;
&lt;li style=&quot;color: #666666; line-height: 21px; margin: 0px 0px 5px 35px; padding: 0px; position: relative;&quot;&gt;Save template.&lt;/li&gt;
&lt;/ol&gt;
&lt;div&gt;
&lt;b style=&quot;font-size: x-large; text-align: left;&quot;&gt;&lt;i&gt;&lt;u&gt;Step :- G&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div&gt;
&lt;b style=&quot;font-size: x-large; text-align: left;&quot;&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div&gt;
&lt;b style=&quot;font-size: x-large; text-align: left;&quot;&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div&gt;
&lt;h3 style=&quot;background-color: white; border-bottom-color: rgb(229, 229, 229); border-bottom-style: solid; border-bottom-width: 1px; color: #111111; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 15px; letter-spacing: -1px; line-height: 18px; margin: 12px 0px 10px; padding: 10px 0px; text-align: justify;&quot;&gt;
&lt;u&gt;&lt;i&gt;How the Meta Description is important in blogger&lt;/i&gt;&lt;/u&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px; text-align: justify;&quot;&gt;
&lt;div style=&quot;color: #666666;&quot;&gt;
As we know about meta descriptions are very important for making blogger seo free as well as seo friendly websites .For making seo friendly Blogger some html changes have been done . These changes to google to index your page as u provide the meta description. Meta descriptions tells to google what site contains . According to meta description google decides the page ranking and page category in google webmaster. For getting High ranking in google search engine meta descriptions as well as meta tags are very important. for this these changes can be done by go to edit html for this follow this&lt;/div&gt;
&lt;span style=&quot;background-color: #eeeeee; font-family: &#39;Source Sans Pro&#39;, sans-serif; font-size: 18px; line-height: 28.796875px; text-align: start;&quot;&gt;&lt;span style=&quot;color: blue;&quot;&gt;Go to Blogger Dashboard&amp;gt;&amp;gt; Settings &amp;gt;&amp;gt; Search preferences &amp;gt; Meta tags &amp;gt; Description and click the Edit link.&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;div style=&quot;color: #666666;&quot;&gt;
and the put meta description&amp;nbsp;&lt;/div&gt;
&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px; text-align: justify;&quot;&gt;
&lt;img alt=&quot; Search Description Feature in Blogger&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEietiYPjdcrRwZFkxbsH-MYw4dfvPajBdVVymn1KN0Z25kPrknmyq_SG_vdQfbREX3CjOGbRgDl0AAQ21TkLqogLVHsfLlzzvE7t3UQKCd5JMeKSs_gOjV2xC4bm0HckBxPLrBM8hE1PvIm/s1600/Add-search-description-for-blogspot.png&quot; height=&quot;198&quot; style=&quot;border: 0px; margin: 0px; padding: 0px;&quot; title=&quot; Search Description Feature in Blogger&quot; width=&quot;270&quot; /&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px; text-align: justify;&quot;&gt;
&lt;b style=&quot;color: black; font-family: &#39;Times New Roman&#39;; font-size: x-large; line-height: normal; text-align: left;&quot;&gt;&lt;i&gt;&lt;u&gt;Step :- H&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; border-bottom-color: rgb(229, 229, 229); border-bottom-style: solid; border-bottom-width: 1px; color: #111111; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 15px; letter-spacing: -1px; line-height: 18px; margin: 12px 0px 10px; padding: 10px 0px; text-align: justify;&quot;&gt;
&lt;i&gt;&lt;u&gt;What is Robots.txt Settings for Blogger&lt;/u&gt;&lt;/i&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px; text-align: justify;&quot;&gt;
The robots.txt file in google is predefined setting but it is not good for making blogger seo free so you need to make some changes in robot.txt file.&lt;br /&gt;
changes can be done by following steps but first you need to clear all about this file.&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px; text-align: justify;&quot;&gt;
Settings &amp;gt; Search Preference &amp;gt; Enable ‘Custom robots.txt’ under ‘Crawlers and indexing’ section and use the below text.&lt;/div&gt;
&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; background-repeat: no-repeat no-repeat; color: #333333; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin: 1em; padding: 1px 10px; text-align: justify;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
User-agent: Mediapartners-Google&lt;br /&gt;
Disallow:&lt;br /&gt;
User-agent: *&lt;br /&gt;
Disallow: /search/&lt;br /&gt;
Disallow: /search?&lt;br /&gt;
Disallow: /search?q=*&lt;br /&gt;
Disallow: /*?updated-max=*&lt;br /&gt;
Disallow: /p/about.html&lt;br /&gt;
Disallow: /p/privacy.html&lt;br /&gt;
Allow: /&lt;/div&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
Sitemap: http://&lt;a href=&quot;http://electronics4projects.blogspot.in/&quot;&gt;http://electronics4projects.blogspot.in/&lt;/a&gt;/atom.xml?redirect=false&amp;amp;start-index=1&amp;amp;max-results=500&lt;/div&gt;
&lt;/blockquote&gt;
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&lt;/h4&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;span style=&quot;color: #666666; font-family: Lucida Sans Unicode, Verdana, Arial, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 14px; line-height: 28px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;b style=&quot;background-color: white; font-size: x-large; text-align: left;&quot;&gt;&lt;i&gt;&lt;u&gt;Step :- I&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: justify;&quot;&gt;
&lt;h3 style=&quot;background-color: white; border-bottom-color: rgb(229, 229, 229); border-bottom-style: solid; border-bottom-width: 1px; color: #111111; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 15px; font-weight: normal; letter-spacing: -1px; line-height: 18px; margin: 12px 0px 10px; padding: 10px 0px;&quot;&gt;
For making seo free blogger you have to Add No Follow Tag to All Labels in your blogger.&lt;/h3&gt;
&lt;div&gt;
Follow these steps&lt;/div&gt;
&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; background-repeat: no-repeat no-repeat; color: #333333; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin: 1em; padding: 1px 10px;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&amp;lt;a expr:href=’data:label.url’ rel=’tag’&amp;gt;&lt;/div&gt;
&lt;/blockquote&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;blockquote style=&quot;background-color: #eeeeee; background-position: 0% 0%; background-repeat: no-repeat no-repeat; color: #333333; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin: 1em; padding: 1px 10px;&quot;&gt;
&lt;div style=&quot;margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&amp;lt;a expr:href=’data:label.url’ rel=’tag,nofollow’&amp;gt;&lt;/div&gt;
&lt;/blockquote&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
Save your template.&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; border-bottom-color: rgb(229, 229, 229); border-bottom-style: solid; border-bottom-width: 1px; color: #111111; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 15px; letter-spacing: -1px; line-height: 18px; margin: 12px 0px 10px; padding: 10px 0px;&quot;&gt;
&lt;u&gt;
Custom Robots Header Tags in blogger&lt;/u&gt;&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
Custom Robots are also very important for making seo friendly blogger .By some changing in &amp;nbsp;Custom Robots you can easily get higher traffic from search engines and peoples&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCb7CZxU06XVE2lBJMQTUsI5pBBIIhyGGFY3RINeMNIDMJpD49U62W2hZlHzKhj3yL_kYeLLSX7AjBbUf8mwcLlWwRu5dFDneDRNkM4CeCC4PyWUD-vOgvlGxIsYBypA0dBFuq_xa4zZg/s1600/yg55.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCb7CZxU06XVE2lBJMQTUsI5pBBIIhyGGFY3RINeMNIDMJpD49U62W2hZlHzKhj3yL_kYeLLSX7AjBbUf8mwcLlWwRu5dFDneDRNkM4CeCC4PyWUD-vOgvlGxIsYBypA0dBFuq_xa4zZg/s640/yg55.jpg&quot; height=&quot;424&quot; width=&quot;640&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;h3 style=&quot;background-color: white; border-bottom-color: rgb(229, 229, 229); border-bottom-style: solid; border-bottom-width: 1px; color: #111111; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 15px; letter-spacing: -1px; line-height: 18px; margin: 12px 0px 10px; padding: 10px 0px;&quot;&gt;
How Sitemap is important in &amp;nbsp;Blogger to Google &amp;amp; Bing&lt;/h3&gt;
&lt;div style=&quot;background-color: white; color: #666666; font-family: &#39;Lucida Sans Unicode&#39;, Verdana, Arial, sans-serif; font-size: 14px; line-height: 28px; margin-bottom: 12px; margin-top: 12px; padding: 0px;&quot;&gt;
Site maps are very important for search engines because of according to site maps google search engines as well as other search engines indexed your pages in their directory list for showing results according to the search tag. site maps are very important to making a site and blogger seo free and seo friendly.&lt;br /&gt;
For this you have to just use google webmaste tools as well as you can use bing webmaster tool for this.&lt;br /&gt;
&lt;br /&gt;
&lt;h2 style=&quot;color: black; font-family: &#39;Times New Roman&#39;; line-height: normal; text-align: left;&quot;&gt;
&lt;u&gt;BLOGGER SEO TIPS AND TRICKS | 10 steps for making blogger seo free | how to make blogger seo friendly&amp;nbsp;&lt;/u&gt;&lt;/h2&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;color: white; font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;Fol&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-size: large;&quot;&gt;&lt;b&gt;&lt;i&gt;&lt;u&gt;&lt;br /&gt;&lt;/u&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;a href=&quot;http://beejmantra.in/&quot;&gt;Astrologer In Jaipur&lt;/a&gt;
&lt;a href=&quot;http://peeyushvashisth.com/&quot;&gt;Astrologer In Jaipur&lt;/a&gt;
&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/7839069301573271129/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2013/09/HOW-TO-MAKE-SEO-FRIENDLY-BLOGGER.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/7839069301573271129'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/7839069301573271129'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2013/09/HOW-TO-MAKE-SEO-FRIENDLY-BLOGGER.html' title='HOW TO MAKE SEO FRIENDLY BLOGGER | SEO TIPS FOR MAKING SITE SEO FREE'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijLWlXV4-9DwdAm0DPz7_lsyIbJbF99wIlqlsJd_cVwWfACMivZWgqz-3dN17zY0hqEjaZziAzRRoF3AaqsF0aY_JUcSJcg5yu_YubjimYoMRMslsdyyhXP0xpCI5JjVM1F_TsRlqDFBM/s72-c/yg55.jpg" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-1361230693331356793</id><published>2013-09-19T05:12:00.001-07:00</published><updated>2013-09-25T01:48:36.689-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="bipolar transistor biasing"/><category scheme="http://www.blogger.com/atom/ns#" term="bipolar transistor characteristics"/><category scheme="http://www.blogger.com/atom/ns#" term="bipolar transistor tutorial"/><category scheme="http://www.blogger.com/atom/ns#" term="npn bipolar transistor"/><category scheme="http://www.blogger.com/atom/ns#" term="pnp bipolar transistor"/><title type='text'>HOW  TO USE A  TRANSISTOR AS AN AMPLIFIER | transistor characteristics and parameters</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;h2 style=&quot;text-align: left;&quot;&gt;
&lt;u&gt;&lt;span style=&quot;color: #741b47;&quot;&gt;HOW TRANSISTOR WORKS AS AN AMPLIFIER&lt;/span&gt;&lt;/u&gt;&lt;/h2&gt;
&lt;div style=&quot;text-align: left;&quot;&gt;
&lt;/div&gt;
&lt;div style=&quot;text-align: left;&quot;&gt;
As we know transistor is a &lt;b&gt;current control device&lt;/b&gt;, it is used for controlling the current in electronics circuits.Transistor is an electronic&amp;nbsp;device used in a circuit to control a large amount of current or voltage with a small amount of voltage or current.  &lt;/div&gt;
Two layers sandwiching one semiconductor between two other &lt;b&gt;semiconductors&lt;/b&gt;.  Because the current is transferred across a material that normally has h&lt;b&gt;igh resistance&lt;/b&gt; (i.e. a &lt;i&gt;resistor&lt;/i&gt;), it was a &lt;b&gt;&quot;transfer-resistor&quot;&lt;/b&gt; or &lt;i&gt;transistor&lt;/i&gt;.&lt;br /&gt;
The first practical &amp;nbsp;transistor was made &amp;nbsp;in &lt;b&gt;1948 &amp;nbsp;&lt;/b&gt;by&amp;nbsp;&lt;b&gt;Shockley&lt;/b&gt;,&lt;br /&gt;
&lt;br /&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;color: #741b47;&quot;&gt;&lt;u&gt;
How a transistor works&lt;/u&gt;&lt;/span&gt;&lt;/h3&gt;
for&amp;nbsp;understanding how a transistor works, you have to understand how semiconductors react to an electric potential.  Some semiconductors will be&lt;b&gt; &lt;i&gt;n&lt;/i&gt;-type&lt;/b&gt;, or negative, which means that free electrons in the &lt;b&gt;material drift&lt;/b&gt; from a negative electrode (of, say, a battery it&#39;s connected to) toward the positive.&lt;br /&gt;
&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Now, we are taking the example of &amp;nbsp;a &lt;i&gt;&lt;b&gt;npn&lt;/b&gt;&lt;/i&gt; transistor.  Each end of the transistor is an &lt;b&gt;&lt;i&gt;n&lt;/i&gt;-type semiconductor material&lt;/b&gt; and between them is an &lt;b&gt;&lt;i&gt;p&lt;/i&gt;-type semiconductor material&lt;/b&gt;.  If you picture such a device plugged into a battery, you&#39;ll see how the transistor works: &lt;br /&gt;
&lt;ul&gt;
&lt;li&gt;We are taking &lt;b&gt;npn transistor&lt;/b&gt; because of in this the&lt;b&gt; mobility of charge carriers&lt;/b&gt; is high as compare to&lt;b&gt; PNP transistor&lt;/b&gt;.&lt;/li&gt;
&lt;li&gt;the &lt;i&gt;n&lt;/i&gt;-type region attached to the negative end of the battery helps propel electrons into the middle &lt;i&gt;p&lt;/i&gt;-type region.
&lt;/li&gt;
&lt;li&gt;the &lt;i&gt;n&lt;/i&gt;-type region attached to the positive end of the battery helps slow electrons coming out of the &lt;i&gt;p&lt;/i&gt;-type region.
&lt;/li&gt;
&lt;li&gt;the &lt;i&gt;p&lt;/i&gt;-type region in the center does both.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;color: #2d2db9; font-family: &amp;quot;Comic Sans MS&amp;quot;; font-size: 28pt; font-style: normal; font-weight: bold; language: en-US; mso-ascii-font-family: &amp;quot;Comic Sans MS&amp;quot;; mso-bidi-font-family: +mj-cs; mso-color-index: 9; mso-fareast-font-family: +mj-ea;&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;color: #2d2db9; font-family: &amp;quot;Comic Sans MS&amp;quot;; font-size: 20pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-font-family: +mj-cs; mso-bidi-language: AR-SA; mso-fareast-font-family: +mj-ea; mso-fareast-language: EN-US;&quot;&gt;&lt;u&gt;PNP BJT Common Emitter Characteristic&lt;/u&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
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&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYd7BXTpERhVRTgxCpmvsw5lGyE50bGq4oXFifEDHMPz3iNscC77f-CyaOg9dcEmKdMj0TLLZ7dd5_n3DhqZgxVhtX4pGBWyxnVllVbBItkyLYFxKIJeU_5ai-OwzwWcSDzD6XJ9GWbmY/s1600/yg.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;HOW TRANSISTOR WORKS AS AN AMPLIFIER&quot; border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYd7BXTpERhVRTgxCpmvsw5lGyE50bGq4oXFifEDHMPz3iNscC77f-CyaOg9dcEmKdMj0TLLZ7dd5_n3DhqZgxVhtX4pGBWyxnVllVbBItkyLYFxKIJeU_5ai-OwzwWcSDzD6XJ9GWbmY/s1600/yg.jpg&quot; height=&quot;257&quot; title=&quot;HOW TRANSISTOR WORKS AS AN AMPLIFIER&quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
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&lt;span style=&quot;color: #2d2db9; font-family: &amp;quot;Comic Sans MS&amp;quot;; font-size: 24pt; font-style: normal; font-weight: bold; language: en-US; mso-ascii-font-family: &amp;quot;Comic Sans MS&amp;quot;; mso-bidi-font-family: +mj-cs; mso-color-index: 9; mso-fareast-font-family: +mj-ea;&quot;&gt;&lt;u&gt;Bipolar Junction Transistors&lt;/u&gt;&lt;/span&gt;&lt;/h2&gt;
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&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzJtcHchl45_nHeBOgwMzD0jeDaMhKwIX6vK_lPGpsHZZi4L-zDW3vuJuOv6W3FcE6wIx0pUoU4r0GOiuPdXE1v7ZBiF9Ks01uGh90cOeyG_pIfwNLvQ97eH8ZpmMs-nmsnD8fPkWehy4/s1600/yg1.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;Bipolar Junction Transistors&quot; border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzJtcHchl45_nHeBOgwMzD0jeDaMhKwIX6vK_lPGpsHZZi4L-zDW3vuJuOv6W3FcE6wIx0pUoU4r0GOiuPdXE1v7ZBiF9Ks01uGh90cOeyG_pIfwNLvQ97eH8ZpmMs-nmsnD8fPkWehy4/s1600/yg1.jpg&quot; height=&quot;239&quot; title=&quot;Bipolar Junction Transistors&quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
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&lt;span style=&quot;color: #2d2db9; font-family: &amp;quot;Comic Sans MS&amp;quot;; font-size: 24pt; font-style: normal; font-weight: bold; language: en-US; mso-ascii-font-family: &amp;quot;Comic Sans MS&amp;quot;; mso-bidi-font-family: +mj-cs; mso-color-index: 9; mso-fareast-font-family: +mj-ea;&quot;&gt;&lt;u&gt;Bipolar Junction Transistors&lt;/u&gt;&lt;/span&gt;&lt;/h2&gt;
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&lt;span style=&quot;color: #0b5394;&quot;&gt;&lt;u&gt;Common Emitter Amplier&lt;/u&gt;&lt;/span&gt;&lt;/h3&gt;
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&lt;b&gt;DC analysis&lt;/b&gt;: An emitter resistor is necessary to provide stability of the bias point. &amp;nbsp;We need to include RE for good biasing (DCsignals) and eliminate it for &lt;b&gt;AC signals&lt;/b&gt;.The solution to include an emitter resistance and use a &quot;&lt;b&gt;bypass&lt;/b&gt;&quot; capacitor to short it out for AC signals as is shown.&lt;/div&gt;
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&lt;span style=&quot;color: #2d2db9; font-family: &amp;quot;Comic Sans MS&amp;quot;; font-size: 24pt; font-style: normal; font-weight: bold; language: en-US; mso-ascii-font-family: &amp;quot;Comic Sans MS&amp;quot;; mso-bidi-font-family: +mj-cs; mso-color-index: 9; mso-fareast-font-family: +mj-ea;&quot;&gt;&lt;span style=&quot;color: #0b5394; font-family: Arial, Helvetica, sans-serif;&quot;&gt;&lt;u&gt;AC analysis of bjt&lt;/u&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;color: #2d2db9; font-family: &amp;quot;Comic Sans MS&amp;quot;; font-style: normal; font-weight: bold; language: en-US; mso-ascii-font-family: &amp;quot;Comic Sans MS&amp;quot;; mso-bidi-font-family: +mj-cs; mso-color-index: 9; mso-fareast-font-family: +mj-ea;&quot;&gt;&lt;span style=&quot;color: #444444; font-family: Times, &amp;quot;Times New Roman&amp;quot;, serif;&quot;&gt;To start the analysis, we kill all DC sources, combine R1 and R2 into RB and replace the BJT with its small signal model. We see that emitter is now common between input and output AC signals (thus, common emitter ampli er. Analysis of this circuit is straightforward. Examination of the circuit shows that:&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;color: #134f5c; font-family: Calibri, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 15px; line-height: 17px;&quot;&gt;&lt;u&gt;BJT current and voltage Equations :-&lt;/u&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h4&gt;
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&lt;span style=&quot;mso-fareast-language: EN-IN; mso-no-proof: yes;&quot;&gt;&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;span style=&quot;color: #134f5c;&quot;&gt;&lt;strong&gt;npn&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;span style=&quot;color: #134f5c;&quot;&gt;pnp&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;span style=&quot;color: #134f5c;&quot;&gt;&lt;span style=&quot;color: black; font-family: Times New Roman;&quot;&gt;

&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;span style=&quot;color: #134f5c;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;b&gt;IE = IB + IC&lt;/b&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;b&gt;&amp;nbsp; IE = IB + IC&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;/span&gt;&lt;/span&gt;
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&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;span style=&quot;color: #134f5c;&quot;&gt;
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&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;span style=&quot;color: black;&quot;&gt;&lt;span style=&quot;font-family: Times New Roman;&quot;&gt;

&lt;span style=&quot;mso-fareast-language: EN-IN; mso-no-proof: yes;&quot;&gt;&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;span style=&quot;font-family: &amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;; font-size: 11pt; line-height: 115%; mso-ansi-language: EN-IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-IN; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-no-proof: yes;&quot;&gt;&lt;b&gt;VCE = -VBC + VBE&amp;nbsp;&lt;/b&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;; font-size: 11pt; line-height: 115%; mso-ansi-language: EN-IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;&quot;&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&lt;b&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/b&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;; font-size: 11pt; line-height: 115%; mso-ansi-language: EN-IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;&quot;&gt;&lt;b&gt;VEC = VEB - VCB &lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;color: #134f5c; font-family: Georgia, &amp;quot;Times New Roman&amp;quot;, serif;&quot;&gt;&lt;u&gt;&lt;em&gt;Modes of Operation of bjt&lt;/em&gt;&lt;/u&gt;&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;strong&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;u&gt;Active region of bjt:&lt;/u&gt;&lt;/span&gt;&lt;/strong&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;u&gt;&amp;nbsp;&lt;/u&gt;&lt;/span&gt;
&lt;/span&gt;&lt;span style=&quot;mso-spacerun: yes;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/h4&gt;
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&lt;span style=&quot;font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;·&lt;span style=&quot;font-size-adjust: none; font-stretch: normal; font: 7pt/normal &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: Calibri;&quot;&gt;Most important mode of operation &lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;&lt;span style=&quot;font-family: Times New Roman;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;·&lt;span style=&quot;font-size-adjust: none; font-stretch: normal; font: 7pt/normal &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: Calibri;&quot;&gt;Central to amplifier operation&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;font-family: Calibri;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;&quot;&gt;&lt;span style=&quot;mso-list: Ignore;&quot;&gt;·&lt;span style=&quot;font-size-adjust: none; font-stretch: normal; font: 7pt/normal &amp;quot;Times New Roman&amp;quot;;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;font-family: Calibri;&quot;&gt;The region where current curves are practically
flat&lt;/span&gt;&lt;/div&gt;
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&lt;div style=&quot;direction: ltr; language: en-IN; margin-bottom: 0pt; margin-top: 14.4pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;&quot;&gt;
&lt;h4 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;color: #99ccff; font-family: Arial; font-weight: bold; language: en-US; mso-ascii-font-family: Arial; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-font-family: +mn-ea; mso-font-kerning: 12.0pt; text-shadow: auto;&quot;&gt;&lt;span style=&quot;font-family: Times, &amp;quot;Times New Roman&amp;quot;, serif;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;span style=&quot;color: black; font-size: large;&quot;&gt;&lt;u&gt;Saturation region of bjt:&lt;/u&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h4&gt;
&lt;br /&gt;
&lt;ul style=&quot;text-align: left;&quot;&gt;
&lt;li&gt;&lt;span style=&quot;color: black; font-family: Times, Times New Roman, serif; font-weight: bold;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;span style=&quot;color: black; font-family: Arial; font-weight: bold;&quot;&gt;&lt;span style=&quot;font-family: Calibri;&quot;&gt;Barrier potential of the junctions cancel each other out causing a
virtualshort&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;&lt;b style=&quot;text-indent: -18pt;&quot;&gt;&lt;br /&gt;&lt;/b&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;h4 style=&quot;text-align: left;&quot;&gt;
&lt;b style=&quot;text-indent: -18pt;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &lt;span style=&quot;font-size: large;&quot;&gt;&amp;nbsp;&lt;u&gt;Cutoff region of bjt&lt;/u&gt; :&lt;/span&gt;&lt;/b&gt;&lt;/h4&gt;
&lt;/div&gt;
&lt;div style=&quot;direction: ltr; language: en-IN; margin-bottom: 0pt; margin-top: 14.4pt; text-align: left; unicode-bidi: embed; vertical-align: baseline;&quot;&gt;
&lt;div style=&quot;direction: ltr; margin-bottom: 0pt; margin-left: 0.25in; margin-top: 12pt; text-indent: -0.25in; unicode-bidi: embed; vertical-align: baseline;&quot;&gt;
&lt;span style=&quot;color: #444444;&quot;&gt;•&lt;span style=&quot;font-family: Arial; font-weight: bold;&quot;&gt;Current reduced to zero&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;direction: ltr; margin-bottom: 0pt; margin-left: 0.25in; margin-top: 12pt; text-indent: -0.25in; unicode-bidi: embed; vertical-align: baseline;&quot;&gt;
&lt;span style=&quot;color: #444444;&quot;&gt;•&lt;span style=&quot;font-family: Arial; font-weight: bold;&quot;&gt;Ideal transistor behaves like an open switch&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0cm 0cm 10pt; text-align: left;&quot;&gt;
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&lt;/div&gt;
&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;/span&gt;&lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0cm 0cm 10pt;&quot;&gt;
&lt;span style=&quot;font-family: Calibri;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;/span&gt;
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&lt;div class=&quot;MsoNormal&quot; style=&quot;margin: 0cm 0cm 10pt;&quot;&gt;
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&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/1361230693331356793/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2013/09/how-to-use-transistor-as-amplifer.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/1361230693331356793'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/1361230693331356793'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2013/09/how-to-use-transistor-as-amplifer.html' title='HOW  TO USE A  TRANSISTOR AS AN AMPLIFIER | transistor characteristics and parameters'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYd7BXTpERhVRTgxCpmvsw5lGyE50bGq4oXFifEDHMPz3iNscC77f-CyaOg9dcEmKdMj0TLLZ7dd5_n3DhqZgxVhtX4pGBWyxnVllVbBItkyLYFxKIJeU_5ai-OwzwWcSDzD6XJ9GWbmY/s72-c/yg.jpg" height="72" width="72"/><thr:total>0</thr:total><georss:featurename>India</georss:featurename><georss:point>20.593684 78.962880000000041</georss:point><georss:box>-8.5815185000000014 37.654286000000042 49.7688865 120.27147400000004</georss:box></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-5540041333588587042</id><published>2013-09-17T10:57:00.002-07:00</published><updated>2013-09-18T08:32:11.556-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="analog circuits"/><category scheme="http://www.blogger.com/atom/ns#" term="ANALOG SIGNALS"/><category scheme="http://www.blogger.com/atom/ns#" term="ANALOG SIGNALS AND LINEAR AMPLIFIERS"/><category scheme="http://www.blogger.com/atom/ns#" term="Innovative Engineering Projects"/><category scheme="http://www.blogger.com/atom/ns#" term="LINEAR AMPLIFIERS"/><category scheme="http://www.blogger.com/atom/ns#" term="THE BIPOLAR LINEAR AMPLIFIER"/><title type='text'>ANALOG SIGNALS AND LINEAR AMPLIFIERS</title><content type='html'>&lt;meta content=’in this all about analog sensors and its working, how analog signals are used, analog signals amplification’ name=’description’/&gt;
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ANALOG SIGNALS AND LINEAR AMPLIFIERS IN ELECTRONICS&lt;/h3&gt;
&lt;div&gt;
&lt;h1 class=&quot;title&quot; style=&quot;background-color: #ccb666; color: #ff1800; font-family: Impact, sans-serif; font-size: 50px; margin: 0px 0px 10px; position: relative; text-align: center; text-shadow: rgba(0, 0, 0, 0.2) 1px 2px 3px;&quot;&gt;
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&lt;b&gt;HOW ANALOG SIGNALS USE THE WORKING PRINCIPLE&amp;nbsp;&lt;/b&gt;&lt;br /&gt;
&lt;br /&gt;
we will be considering signals, &lt;u&gt;&lt;b&gt;analog circuits&lt;/b&gt;&lt;/u&gt;, and &lt;b&gt;&lt;u&gt;ampliﬁers&lt;/u&gt;&lt;/b&gt;. Asignal contains some type of information.&lt;br /&gt;
For example, sound waves produced by a speaking human contain the information the person is conveying to another person.&lt;br /&gt;
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&lt;br /&gt;
Our physical senses, such as hearing, vision, and touch, are naturally analog. &lt;b&gt;&lt;u&gt;Analog&lt;/u&gt;&lt;/b&gt;&lt;br /&gt;
&lt;b&gt;&lt;u&gt;signals&lt;/u&gt;&lt;/b&gt; can represent parameters such as &lt;b&gt;temperature&lt;/b&gt;, &lt;b&gt;pressure&lt;/b&gt;, and &lt;b&gt;wind velocity&lt;/b&gt;.&lt;br /&gt;
Here, we are interested in electrical signals, such as the output signal from a compact&lt;br /&gt;
disc, a signal from a microphone, or a signal from a heart rate monitor. The electrical&lt;br /&gt;
signals are in the form of time-varying currents and voltages.&lt;br /&gt;
&lt;br /&gt;
The magnitude of an &lt;b&gt;&lt;u&gt;analog signal&lt;/u&gt;&lt;/b&gt; can take on any value within limits and may vary continuously with time. &lt;b&gt;&lt;u&gt;Electronic circuits&lt;/u&gt;&lt;/b&gt; that process analog signals are called &lt;b&gt;&lt;u&gt;analog circuits&lt;/u&gt;&lt;/b&gt;. One example of an analog circuit is a linear ampliﬁer. A linear &lt;b&gt;&lt;u&gt;ampliﬁer&lt;/u&gt;&lt;/b&gt; magniﬁes an input signal and produces an output signal whose magnitude is larger and directly proportional to the input signal.&lt;br /&gt;
&lt;br /&gt;
In many modern day systems, signals are processed, transmitted, or received in digital form. In order to produce an analog signal, these digital signals need to be processed through a digital-to-analog (D/A) converter. D/A and A/D (analog-to digital) converters are considered . In this chapter, we will assume that&lt;br /&gt;
we already have an analog signal that needs to be ampliﬁed.Time-varying signals from a particular source very often need to be ampliﬁed before the signal is capable of being “useful.” For example, Figure 6.1 shows a signal source that is the output of a compact disc system. We assume the signal source is the output of the D/A converter and this signal consists of a small time-varying voltage and current, which means the signal power is relatively small.&lt;br /&gt;
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&lt;br /&gt;
The power required to drive the speakers is larger than the output signal from the compact disc, so the compact disc signal must be ampliﬁed before it is capable of driving the speakers in order that sound can be heard. Other examples of signals that must be ampliﬁed before they are capable of driving loads include the output of a microphone, voice signals received on earth from an orbiting manned shuttle, video signals from&lt;br /&gt;
an orbiting weather satellite, and the output of an EKG.&lt;br /&gt;
&lt;br /&gt;
Also shown in Figure 6.1 is a dc voltage source connected to the ampliﬁer. The ampliﬁer contains transistors that must be biased in the forward-active region so that the transistors can act as amplifying devices.&lt;br /&gt;
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New Electronic Inventions&lt;/div&gt;
&lt;div dir=&quot;ltr&quot;&gt;
Inventors, Jung Won Seo, Jae-Woo Park, Keong Su Lim, Ji-Hwan Yang and Sang Jung Kang, who are scientists at the Korean Advanced Institute of Science and Technology, have created the world&#39;s first transparent computer chip.The chip, known as (TRRAM) or transparent resistive random access memory, is similar to existing chips known as (CMOS) or metal-oxide semiconductor memory, which we use in&amp;nbsp;new electronics.The difference is that TRRAM is completely clear and transparent. What is the benefit of having transparency?&quot;It is a new milestone of transparent electronic systems,&quot; says Jung Won Seo. &quot;By integrating TRRAM with other transparent electronic components, we can create a total see-through embedded electronic systems.&quot;The technology could enable the windows or mirrors in your home to be used as computer monitors and television screens.This technology is expected to be available within 3 to 4 years.Source:&amp;nbsp;&lt;/div&gt;
&lt;h3 class=&quot;grn_heading&quot; style=&quot;background-color: white; color: #993333; font-family: Tahoma, Arial, Helvetica, Verdana, sans-serif; font-size: 14px; margin: 0px 0px 2px;&quot;&gt;
WaterBean Purifies Tap Water, Saves Bottles&lt;/h3&gt;
&lt;div class=&quot;loading starbox&quot; id=&quot;inventionScore7331&quot; style=&quot;background-color: white; color: #333333; float: right; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; margin-left: 6px; margin-top: -2px; text-align: justify;&quot;&gt;
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&lt;div style=&quot;cursor: pointer; height: 20px; left: 56px; position: absolute; top: 0px; width: 14px;&quot;&gt;
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&lt;i style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot;&gt;Jul-31-13&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot;&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;span style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot;&gt;Designed to help reduce plastic bottle waste, the WaterBean will purify tap water—encouraging water worriers to reuse the same plastic bottle for a longer time.&lt;/span&gt;&lt;br /&gt;
&lt;br style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot; /&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot;&gt;The WaterBean contracts and expands to fit inside almost any water bottle, and its exchangeable filters remain active for up to three months (or 140 liters of water). The filters are made from non-toxic, activated coconut carbon, which the developers claim will remove chlorine odors and off tastes while also adding magnesium to the water. To use, simply drop the device inside the water bottle, then shake and swirl.&lt;/span&gt;&lt;br /&gt;
&lt;br style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot; /&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: verdana, tahoma, arial, sans-serif; font-size: 12px; text-align: justify;&quot;&gt;While the WaterBean will not purify dirty water, it will help to improve the taste and odor of tap water, with one filter potentially saving 280 plastic bottles from landfills. The developers are currently seeking funding for their project on Indiegogo.&lt;/span&gt;&lt;/div&gt;
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Smartbox Technology&lt;/div&gt;
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Insurance companies are implementing smartbox technology so good drivers can benefit from cheap insurance rates.The smartbox, similar to a black box for airplanes, records details about how your car is driven, which can result in cheap car insurance for responsible drivers.The device is connected to the electronics in your car and collects a wide criteria of information such as time, speed, braking, cornering, acceleration and location.The smartbox data is wireless transferred in real time to the insurance company and provides a profile of when, where and how you drive. This profile is then used to compare insurance rates and to reward low-risk driving behavior with cheap insurance rates.Drivers are high-risk when they drive irresponsibly such as speeding, frequent lane changing, driving in high-risk locations or at high-risk times such as in heavy traffic or late at night.These new electronic inventions are intended to replace the standard practice of categorizing drivers into group behavior to determine insurance coverage and premium payments.For example, young drivers are more likely to drive fast, drive at night. and use a cell phone while driving. Statistically, young drivers are more likely to cause an accident so insurance companies charge them higher rates to cover the costs of accident claims.SEE RELATED ARTICLE ABOUT SMARTBOX INSURANCESo even if you&#39;re a young, responsible driver, you will pay high insurance rates because of group behavior.This technology allows you to provide proof that your driving behavior doesn&#39;t fit the pattern of your demographic group.All the information collected about your driving can be viewed online - including what you&#39;re doing well and what could be improved. Your insurance premium is then calculated according to your driving profile.Sources:&amp;nbsp;&lt;/div&gt;
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Electronic Pills - Collecting Data Inside The Body&lt;/div&gt;
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After years of&amp;nbsp;investment&amp;nbsp;and development, wireless devices contained in swallowable capsules are now reaching the market.Companies such as SmartPill based in Buffalo, New York and Israel-based Given Imaging (PillCam) market capsules the size of vitamin tablets.These pills contain sensors or tiny cameras that collect information as they travel through the gastrointestinal tract before being excreted from the body a day or two later.These new electronic inventions transmit information such as acidity, pressure and temperature levels or images of the esophagus and intestine to your doctor&#39;s computer for analysis.Doctors often use invasive methods such as catheters, endoscopic instruments or radioisotopes for collecting information about the digestive tract. So device companies have been developing easier, less intrusive ways, to gather information.Digestive diseases and disorders can include symptoms such as acid reflux, bloating, heartburn, abdominal pain, constipation, difficulty swallowing or loss of appetite.&quot;One of the main challenges is determining just what is happening in the stomach and intestines.&quot; says Dr. Anish A. Sheth, Director of the Gastrointestinal Motility Program at Yale-New Haven Hospital.Doctors can inspect the colon and peer into the stomach using endoscopic instruments. But some areas cannot be easily viewed, and finding out how muscles are working can be difficult.Electronic pills are being used to measure muscle contraction, ease of passage and other factors to reveal information unavailable in the past.Sources:&amp;nbsp;&lt;/div&gt;
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Digital Pen&lt;/div&gt;
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A digital pen is one of the new electronic inventions that can help us record information.Despite the digital age, we still use pens. But it would be great to have our handwritten notes and drawings digitally recorded without having to use a scanner.The Zpen from Dane-Elec is a wireless pen that uses a clip-on receiver to digitally record what you write.It uploads the information to your computer where it can be viewed, edited and filed as a word processing document.The digital pen utilizes character recognition software and works by recording movement. Features include profile creation, a dictionary and fifteen language options.Source:&amp;nbsp;&lt;/div&gt;
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Instant Prints&lt;/div&gt;
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Creating instant prints from a digital camera is one of the new electronic inventions in printing. The Polaroid PoGo™ is a small portable printer that weighs only a few ounces.The printer produces full color 2&quot; x 3&quot; prints using an &quot;inkless&quot; technology. The images are created from heat activated crystals in the photo paper. The photos are water proof, tear proof and smear proof.This new electronic invention connects to a digital camera using a USB cable, or to a mobile phone through wireless Bluetooth. It uses rechargeable batteries or an AC adapter.- See more at:&amp;nbsp;&lt;/div&gt;
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&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/3882997481301120435/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2013/07/new-electronic-inventions-inventors.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/3882997481301120435'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/3882997481301120435'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2013/07/new-electronic-inventions-inventors.html' title='New Electronic Inventions | How  They Are Applicable  In Electronics'/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-7378216391395934007</id><published>2013-07-26T22:01:00.004-07:00</published><updated>2014-03-13T23:28:05.828-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="8051c with peripherals"/><category scheme="http://www.blogger.com/atom/ns#" term="adc0808 interfacing"/><category scheme="http://www.blogger.com/atom/ns#" term="how to interface 8051 with adc"/><category scheme="http://www.blogger.com/atom/ns#" term="microcontroller with adc0808"/><title type='text'>How To Use Adc With 8051 Microcontroller In Proteus </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
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How to interface adc0808 with 8051 microcontroller&lt;br /&gt;
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&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;The following circuit &amp;nbsp;diagram &lt;/span&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;shows the required 8051 microcontroller circuit.&lt;/span&gt;&lt;br /&gt;
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&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI_3JKUILdSYIyEJqijIVAvLpXCFHTs0hczgaDHtHQ3SR0MezCAVn2yRB8sUeGdOE28H9hFnxZWAO2Ls3e6gB6r2S0ZTLtE5i1iSU8lZjwkH9pa1foTV-pV6Bf9EeterBSM8n7sjbcjTs/s1600/8051+ADC+CCT.JPG&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;how to use adc with 8051 microcontroller &quot; border=&quot;0&quot; height=&quot;187&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI_3JKUILdSYIyEJqijIVAvLpXCFHTs0hczgaDHtHQ3SR0MezCAVn2yRB8sUeGdOE28H9hFnxZWAO2Ls3e6gB6r2S0ZTLtE5i1iSU8lZjwkH9pa1foTV-pV6Bf9EeterBSM8n7sjbcjTs/s320/8051+ADC+CCT.JPG&quot; title=&quot;how to use adc with 8051 microcontroller in proteus &quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
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&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;In this &amp;nbsp;circuit, 8 bit data bus of ADC0808 is attached with 8051 on Port 0. control signals of ADC0808 are connected &amp;nbsp;on Port 2 of 8051 micro controller. LCD is connected on Port &amp;nbsp;1, LCD is used to show the output &amp;nbsp;of ADC.&lt;/span&gt;&lt;/div&gt;
&lt;br style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot; /&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ADC0808 has 8 input channels so at a time 8 sensors can be connected. You can use any channel for ADC purposes in the code. A potentiometer (i-e variable 10k resistor) is connected on IN1&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;of ADC0808 just to&amp;nbsp;demonstrate&amp;nbsp;how to use this code. Input voltage at IN1 is read in the code and displayed on the LCD. &amp;nbsp;ADC0808 gives an output of 8bit value, so a voltage value of 0v at IN1 will mean ADC value of 0 and a voltage of 5v at IN1 pin means ADC value of 255. In the above figure, it is clear that a voltage of 2.5v is applied on IN1 pin and ADC value of 127 (i-e half of 255) is displayed on the LCD correctly.&lt;/span&gt;&lt;br /&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;A crystal of 12MHz value is used in this circuit, which makes this 8051 (i-e AT89C51) run at a speed of 1MIPS .&lt;/span&gt;&lt;br /&gt;
&lt;h3 style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-weight: bolder; margin: 0.83em 0px; padding: 0px; position: relative;&quot;&gt;
&lt;span style=&quot;color: #38761d; font-size: large;&quot;&gt;Code&lt;/span&gt;&lt;/h3&gt;
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&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;The code is shown below.&lt;/span&gt;&lt;/div&gt;
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&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja_lZxIqYuuoflOxOT12K6aPG-16OPU9Ia84Lj-sAzLPslla2K2kY2_OT90Eqz6LxMaE8OmjFTMtR2DIUSC6pkrjUARvec3UOiE4f0g1lLGuWjQ3Z5OmIyU8S72AXuil5XMZpaAIsLbkk/s1600/8051+ADC+MAIN+CODE.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;8051 codes for adc0808&quot; border=&quot;0&quot; height=&quot;230&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja_lZxIqYuuoflOxOT12K6aPG-16OPU9Ia84Lj-sAzLPslla2K2kY2_OT90Eqz6LxMaE8OmjFTMtR2DIUSC6pkrjUARvec3UOiE4f0g1lLGuWjQ3Z5OmIyU8S72AXuil5XMZpaAIsLbkk/s320/8051+ADC+MAIN+CODE.jpg&quot; title=&quot;8051 coading&quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
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&lt;div class=&quot;separator&quot; style=&quot;background-color: white; clear: both; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px; text-align: center;&quot;&gt;
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&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;In the main function, firstly pins attached with ADC0808 are initialized using&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;InitADC();&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;statement, then LCD is initialized using&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;InitLCD()&amp;nbsp;&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;function. Then &quot;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;Starting...&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&quot; is displayed on the LCD for one second. After that LCD screen is cleared.&lt;/span&gt;&lt;/div&gt;
&lt;br style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot; /&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;In the&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;while(1)&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;loop,&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ADC_Value = ReadADC(AN1);&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;statement reads value from IN1 pin of ADC0808 and assigns this value to&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ADC_Value&amp;nbsp;&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;variable. Next 3 statements are converting&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ADC_Value&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;in to digits, which will be displayed on the LCD screen. After that, LCD screen is cleared and ADC value is&amp;nbsp;displayed&amp;nbsp;on the LCD.&lt;/span&gt;&lt;br /&gt;
&lt;br style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot; /&gt;
&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;InitADC()&amp;nbsp;&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;function is shown below.&lt;/span&gt;&lt;br /&gt;
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&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;In the&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;InitADC()&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;function shown above, pins attached to ADC0808 are&amp;nbsp;initialized properly. Also, data bus attached with Port 0&amp;nbsp;is initialized as well.&lt;/span&gt;&lt;/div&gt;
&lt;br style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot; /&gt;
&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ReadADC()&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;function code is shown below.&lt;/span&gt;&lt;br /&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdnTIBAzg2Lg51hRTaJmbgOUM2lzxcwXazQoAAF1iHq7ETQNH150UmrPGrvzPLS3OyJsTzdiUYkm0eqiw1CeO4CI2NjHxsEHBTDPcx9gaJSoQIui0o493SQob0oNmbG_j72FBwoN4eros/s1600/8051+READ+ADC+CODE.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img alt=&quot;adc0808&quot; border=&quot;0&quot; height=&quot;320&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdnTIBAzg2Lg51hRTaJmbgOUM2lzxcwXazQoAAF1iHq7ETQNH150UmrPGrvzPLS3OyJsTzdiUYkm0eqiw1CeO4CI2NjHxsEHBTDPcx9gaJSoQIui0o493SQob0oNmbG_j72FBwoN4eros/s320/8051+READ+ADC+CODE.jpg&quot; title=&quot;adc0808&quot; width=&quot;132&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both;&quot;&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
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&lt;/div&gt;
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&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ReadADC()&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;function (shown above) returns 8 bit ADC value. This value is read from a channel, which is the input&amp;nbsp;argument&amp;nbsp;to&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ReadADC()&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;&amp;nbsp;function. Channel can have a value of AN0 for IN0 pin of ADC0808 or AN1 for IN1 pin etc. For example, to read voltage value at IN7 pin of ADC0808, you can use the statement&amp;nbsp;&lt;/span&gt;&lt;i style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;ReadADC(AN7);&lt;/i&gt;&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;.&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both;&quot;&gt;
&lt;span style=&quot;background-color: white; color: #333333; font-family: &#39;Helvetica Neue Light&#39;, HelveticaNeue-Light, &#39;Helvetica Neue&#39;, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px;&quot;&gt;This is all about 8051 with adc0808&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;/div&gt;
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&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/7378216391395934007/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2013/07/adc-interfacing-with-8051.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/7378216391395934007'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/7378216391395934007'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2013/07/adc-interfacing-with-8051.html' title='How To Use Adc With 8051 Microcontroller In Proteus '/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI_3JKUILdSYIyEJqijIVAvLpXCFHTs0hczgaDHtHQ3SR0MezCAVn2yRB8sUeGdOE28H9hFnxZWAO2Ls3e6gB6r2S0ZTLtE5i1iSU8lZjwkH9pa1foTV-pV6Bf9EeterBSM8n7sjbcjTs/s72-c/8051+ADC+CCT.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-7402096489957706142.post-4842745467187889121</id><published>2013-07-16T19:50:00.000-07:00</published><updated>2013-09-25T18:48:52.999-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="easy circuit"/><category scheme="http://www.blogger.com/atom/ns#" term="electronics projects"/><category scheme="http://www.blogger.com/atom/ns#" term="ldr sensor for color detction"/><category scheme="http://www.blogger.com/atom/ns#" term="ldr with color sensor"/><category scheme="http://www.blogger.com/atom/ns#" term="led with sensor"/><category scheme="http://www.blogger.com/atom/ns#" term="sensors for projects"/><category scheme="http://www.blogger.com/atom/ns#" term="using op-amp color sensor"/><title type='text'>Color Detection Using LDR | Sensor Using LDR | Sensors theory of working | Light Sensors | Street Light Project </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
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&lt;br /&gt;
&lt;h2 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;border: 0px; color: #333333; font-family: Arial; font-size: 12px; line-height: 18px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-size: xx-small; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-size: 13px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;LDR SENSOR FOR COLOR DETECTION&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
&lt;h3 style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;border: 0px; color: #333333; font-family: Arial; font-size: 12px; line-height: 18px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-size: xx-small; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-size: 13px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;summary:-&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h3&gt;
&lt;div style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;border: 0px; color: #333333; font-family: Arial; line-height: 18px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;This circuit can be used to sense and differentiate between different colors. This project demonstrates the principle and operation of a simple color sensor using&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;border: 0px; color: #333333; font-family: Tahoma, Arial, sans-serif; line-height: 20px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;LDR&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;. The circuit is divided into three parts: Detector (LDR), Comparator and Output. This circuit is based on LM324 IC whose pin diagram has been shown below:&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;text-align: left;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;border: 0px; color: #333333; font-family: Tahoma, Arial, sans-serif; line-height: 20px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;border: 0px; color: #333333; line-height: 20px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-family: Verdana, sans-serif; font-size: large; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;b&gt;&lt;u&gt;&lt;i&gt;Circuit diagram:-&lt;/i&gt;&lt;/u&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div&gt;
&lt;span style=&quot;border: 0px; color: #333333; font-family: Tahoma, Arial, sans-serif; font-size: xx-small; line-height: 20px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-family: Arial; font-size: 13px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;border: 0px; font-size: 13px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;background-color: white; clear: both; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px; text-align: center;&quot;&gt;
&lt;a href=&quot;http://www.gophoto.it/view.php?i=https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnHSk77e6Yz8EDw_SjyEGIfdp0RalDhnPrleSO-G92EQ-E3rZtpQsLvFlSkIiMUaxEhmRT3bPi8Cf1F_9EjH8G4UKE2eP8uRQvZj2rGgohG8QUB8klAyWivRHcUqhjV8Wh2TQqdsoiYg8/s1600/ldr.gif&quot; imageanchor=&quot;1&quot; style=&quot;color: #6699cc; margin-left: 1em; margin-right: 1em; text-decoration: none;&quot;&gt;&lt;img alt=&quot;ldr colour detection&quot; border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnHSk77e6Yz8EDw_SjyEGIfdp0RalDhnPrleSO-G92EQ-E3rZtpQsLvFlSkIiMUaxEhmRT3bPi8Cf1F_9EjH8G4UKE2eP8uRQvZj2rGgohG8QUB8klAyWivRHcUqhjV8Wh2TQqdsoiYg8/s320/ldr.gif&quot; height=&quot;296&quot; style=&quot;border: none; position: relative;&quot; title=&quot;sensor using ldr&quot; width=&quot;320&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;background-color: white; clear: both; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px; text-align: center;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;background-color: white; clear: both; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px; text-align: center;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;separator&quot; style=&quot;background-color: white; clear: both; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px; text-align: center;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; border: 0px; color: #333333; line-height: 24px; margin: 0px 0px 0.0001pt; outline: 0px; padding: 0px; text-align: justify;&quot;&gt;
&lt;b style=&quot;background-color: transparent; line-height: 26px;&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: large;&quot;&gt;Component:-&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; border: 0px; color: #333333; line-height: 20px; margin: 0px 0px 0.0001pt; outline: 0px; padding: 0px; text-align: justify;&quot;&gt;
&lt;ol style=&quot;font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;&quot;&gt;
&lt;li style=&quot;margin: 0px 0px 0.25em; padding: 0px;&quot;&gt;&lt;span style=&quot;font-family: Arial;&quot;&gt;&lt;span style=&quot;font-size: large; line-height: 25.98958396911621px;&quot;&gt;&lt;b&gt;Resistor&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;margin: 0px 0px 0.25em; padding: 0px;&quot;&gt;&lt;span style=&quot;font-family: Arial;&quot;&gt;&lt;span style=&quot;font-size: large; line-height: 25.98958396911621px;&quot;&gt;LED&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;margin: 0px 0px 0.25em; padding: 0px;&quot;&gt;&lt;span style=&quot;font-family: Arial; font-size: large;&quot;&gt;LDR&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;margin: 0px 0px 0.25em; padding: 0px;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;Preset&lt;/span&gt;&lt;/li&gt;
&lt;li style=&quot;margin: 0px 0px 0.25em; padding: 0px;&quot;&gt;&lt;span style=&quot;font-size: large;&quot;&gt;IC LM324&lt;/span&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;b&gt;&lt;span style=&quot;font-size: large;&quot;&gt;&lt;u&gt;&lt;span style=&quot;font-family: Verdana, sans-serif;&quot;&gt;Description of making LDR Sensor&lt;/span&gt;&lt;/u&gt;&lt;span style=&quot;font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;&quot;&gt; :-&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div style=&quot;background-color: white; border: 0px; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 20px; margin: 0px 0px 0.0001pt; outline: 0px; padding: 0px; text-align: justify;&quot;&gt;
&lt;div style=&quot;border: 0px; font-family: Tahoma, Arial, sans-serif; line-height: 18px; margin-bottom: 15px; margin-top: 15px; outline: 0px; padding: 0px;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;In this project, when light of a particular color falls on&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;b&gt;LDR&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;, its &lt;b&gt;resistance decreases&lt;/b&gt; and an output voltage is produced. This voltage is dependent on the intensity and wavelength of different color. For this we need to set reference voltage of comparator according to our requirement.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div style=&quot;border: 0px; font-family: Tahoma, Arial, sans-serif; line-height: 24px; margin: 0px 0px 0.0001pt; outline: 0px; padding: 0px;&quot;&gt;
&lt;span style=&quot;font-size: large;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;For Eg., If we set reference voltage at positive pin with 0.38volts, the LDR becomes sensitive to blue light. When blue light falls on the&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;LED&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;,&lt;/span&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&amp;nbsp;an output of approximate voltage 0.28V is produced, this glows the output LED.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;But if we use a yellow color light on LDR then input voltage at the comparator is around 0.7 volts at the negative pin of comparator and the output LED doesn’t glow.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;h2&gt;
&lt;span style=&quot;background-color: transparent; border: 0px; font-family: Arial; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;&lt;span style=&quot;background-color: transparent; border: 0px; font-size: large; line-height: 26px; margin: 0px; outline: 0px; padding: 0px;&quot;&gt;HOW LDR CHANGES RESISTANCE WITH LIGHT.&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h2&gt;
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&lt;div class=&quot;blogger-post-footer&quot;&gt;Innovative Engineering Projects&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://electronics4projects.blogspot.com/feeds/4842745467187889121/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://electronics4projects.blogspot.com/2013/07/color-detction-using-ldr-sensor-using.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/4842745467187889121'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/7402096489957706142/posts/default/4842745467187889121'/><link rel='alternate' type='text/html' href='http://electronics4projects.blogspot.com/2013/07/color-detction-using-ldr-sensor-using.html' title='Color Detection Using LDR | Sensor Using LDR | Sensors theory of working | Light Sensors | Street Light Project '/><author><name>Yogesh</name><uri>http://www.blogger.com/profile/03553198909503880123</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnHSk77e6Yz8EDw_SjyEGIfdp0RalDhnPrleSO-G92EQ-E3rZtpQsLvFlSkIiMUaxEhmRT3bPi8Cf1F_9EjH8G4UKE2eP8uRQvZj2rGgohG8QUB8klAyWivRHcUqhjV8Wh2TQqdsoiYg8/s72-c/ldr.gif" height="72" width="72"/><thr:total>1</thr:total></entry></feed>