{"id":65257,"date":"2022-10-05T20:16:54","date_gmt":"2022-10-05T14:46:54","guid":{"rendered":"https:\/\/www.oliveboard.in\/blog\/?p=65257"},"modified":"2022-10-10T11:26:55","modified_gmt":"2022-10-10T05:56:55","slug":"how-to-solve-percentage-questions-quickly","status":"publish","type":"post","link":"https:\/\/www.oliveboard.in\/blog\/how-to-solve-percentage-questions-quickly\/","title":{"rendered":"Tips and tricks to solve questions on percentages and ratios quickly"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_77 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of content<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.oliveboard.in\/blog\/how-to-solve-percentage-questions-quickly\/#Solving_ratio_questions_quickly_Important_points\" >Solving ratio questions quickly: Important points<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.oliveboard.in\/blog\/how-to-solve-percentage-questions-quickly\/#How_to_solve_percentage_questions_quickly\" >How to solve percentage questions quickly<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.oliveboard.in\/blog\/how-to-solve-percentage-questions-quickly\/#FAQs\" >FAQs<\/a><\/li><\/ul><\/nav><\/div>\n<div class=\"yoast-breadcrumbs\"><span><span><a href=\"https:\/\/www.oliveboard.in\/blog\/\">Home<\/a><\/span> \u00bb <span><a href=\"https:\/\/www.oliveboard.in\/blog\/category\/exam-hacks\/\">Tips &amp; Tricks<\/a><\/span> \u00bb <span class=\"breadcrumb_last\" aria-current=\"page\"><strong>Solve percentage and ratio questions faster<\/strong><\/span><\/span><\/div>\n\n\n<p><a href=\"https:\/\/www.oliveboard.in\/sbi-po-mock-test\/?ref=contsp&amp;utm_medium=Organic&amp;utm_source=blog&amp;utm_campaign=contsp\" target=\"_blank\" rel=\"noreferrer noopener\">SBI PO<\/a> and <a href=\"https:\/\/www.oliveboard.in\/ssc-cgl-tier-1-mock-test\/?ref=contsp-ssc&amp;utm_medium=Organic&amp;utm_source=blog&amp;utm_campaign=contsp-ssc\" target=\"_blank\" rel=\"noreferrer noopener\">SSC CGL<\/a> are around the corner. Percentages and ratios form the base for solving questions from many topics (data interpretation, age problems, simplification, etc.) and hence it becomes an important topic for quantitative section of any exam whether it is SSC, RRB or Banking. The questions based on these topics are usually easy and thus the speed of solving a question is based on how quickly you can solve these questions. In today\u2019s blog we will be discussing on how to solve percentage questions quickly.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.oliveboard.in\/sbi-po-mock-test\/?ref=contsp&amp;utm_medium=Organic&amp;utm_source=blog&amp;utm_campaign=contsp\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt a FREE SBI PO Mock Test here<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.oliveboard.in\/ssc-cgl-mock-test\/?ref=contsp-ssc&amp;utm_medium=Organic&amp;utm_source=Blog&amp;utm_campaign=contsp-ssc\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt a Free SSC CGL New Pattern Mock Test Here<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solving_ratio_questions_quickly_Important_points\"><\/span><strong>Solving ratio questions quickly: Important points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Ratio indicates how many times one number contains another.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Combined ratio from individual ratio<\/strong><\/h3>\n\n\n\n<p>If A:B = a:b<sub>1<\/sub> and B:C = b<sub>2<\/sub>:c then, A:B:C =(a*b<sub>2<\/sub>):(b<sub>1<\/sub>*b<sub>2<\/sub>):(b<sub>1<\/sub>*c)<\/p>\n\n\n\n<p>Similarly,<\/p>\n\n\n\n<p>If A:B = a:b<sub>1<\/sub>, B:C = b<sub>2<\/sub>:c<sub>1<\/sub> and C:D = c<sub>2<\/sub>:d then, A:B:C:D = (a*b<sub>2<\/sub>*c<sub>2<\/sub>): (b<sub>1<\/sub>*b<sub>2<\/sub>*c<sub>2<\/sub>):(b<sub>1<\/sub>*c<sub>1<\/sub>*c<sub>2<\/sub>):(b<sub>1<\/sub>*c<sub>1<\/sub>*d)<\/p>\n\n\n\n<p><strong>Example: <\/strong>If A:B = 1:2, B:C = 3:7 and C:D = 4:5 then A:B:C:D =<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignleft\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"120\" src=\"https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2020\/11\/percentage1.png\" alt=\"Solve ratio questions quickly\" class=\"wp-image-65258\"\/><\/figure><\/div>\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>A:B:C:D = (1*3*4):(2*3*4):(2*7*4):(2*7*5) =12:24:56:70 = 6:12:28:35<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>If the difference between two quantities remains the same<\/strong><\/h3>\n\n\n\n<p>Let us understand this concept through examples. This is helpful especially in age problems.<\/p>\n\n\n\n<p><strong>Example 1(Illustration): <\/strong>The ratio of number of boys to the number of girls in a school is 5:4. If 60 more students are admitted in the school such that the difference between number of boys and girls remains the same, the ratio becomes 13:11. What is the total number of students in the school?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Initial ratio = 5:4, (Difference = 1)<\/p>\n\n\n\n<p>Final ratio = 13:11, (Difference = 2)<\/p>\n\n\n\n<p>The difference between number of boys and girls remains the same. Hence, the initial ratio should be multiplied by 2<\/p>\n\n\n\n<p>Initial ratio * 2 =10:8, (Difference = 2)<\/p>\n\n\n\n<p>Final ratio * 1 = 13:11, (Difference = 2)<\/p>\n\n\n\n<p>Initially let number of boys = 10x then, number of girls = 8x<\/p>\n\n\n\n<p>After the admission of 60 students, Number of boys = 13x and Number of girls = 11x<\/p>\n\n\n\n<p>Since difference remains the same, Number of girls who were newly admitted to the school = Number of boys who were newly admitted to the school = 30<\/p>\n\n\n\n<p>Number of girls who were newly admitted to the school = 11x &#8211; 8x = 3x = 30<\/p>\n\n\n\n<p>x=10<\/p>\n\n\n\n<p>Hence initially there was (10+8)x students = 180 students.<\/p>\n\n\n\n<p><strong>Example 2: <\/strong>Current age of father and daughter is in the ratio 2:1, while the current age of daughter and granddaughter is in the ratio of 8:1. If the age of father and daughter will be in the ratio 13:7 after 4 years, then what will be the age of the granddaughter after 4 years?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Age of father and daughter<\/p>\n\n\n\n<p>Initial ratio= (2:1)*(6:6) = 12:6<\/p>\n\n\n\n<p>Final ratio = (13:7)*1 = 13:7<\/p>\n\n\n\n<p>13x-12x = x = 4 years<\/p>\n\n\n\n<p>Hence present age of daughter= 24 years<\/p>\n\n\n\n<p>Present age of granddaughter = 24\/8 = 3 years<\/p>\n\n\n\n<p>Hence age of granddaughter after 4 years = 3+4 = 7 years<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.oliveboard.in\/sbi-po-mock-test\/?ref=contsp&amp;utm_medium=Organic&amp;utm_source=blog&amp;utm_campaign=contsp\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt a Free SBI PO Mock Test here<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.oliveboard.in\/ssc-cgl-mock-test\/?ref=contsp-ssc&amp;utm_medium=Organic&amp;utm_source=Blog&amp;utm_campaign=contsp-ssc\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt a Free SSC CGL New Pattern Mock Test here<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"How_to_solve_percentage_questions_quickly\"><\/span><strong>How to solve percentage questions quickly<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Percentage is a number or ratio&nbsp;expressed as a fraction of 100. While solving problems, converting the percentages into fractions will save a lot of calculation and hence reduce the time required for solving. The table below depicts some percentages to fractions conversion:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignleft\"><img loading=\"lazy\" decoding=\"async\" width=\"880\" height=\"514\" src=\"https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2020\/11\/percentage2.png\" alt=\"Solve percentage questions quickly\" class=\"wp-image-65259\"\/><\/figure><\/div>\n\n\n<p>Apart from the above table, the following points are also important.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Successive increase or decrease<\/strong><\/h3>\n\n\n\n<p>This is helpful for profit and loss, problems on depreciations, etc.<\/p>\n\n\n\n<p>In case of successive increase or decrease of x% and y% respectively, we have<\/p>\n\n\n\n<p><strong>Effective increase or decrease = {(100 + x)\/100 * (100+y)\/100 \u2013 1} * 100% = x + y + (x*y)\/100<\/strong><\/p>\n\n\n\n<p>NOTE: Increase is represented as +ve and decrease as \u2013ve<\/p>\n\n\n\n<p>Similarly,<\/p>\n\n\n\n<p>In case of successive increase or decrease of x%, y% and z% respectively, we have<\/p>\n\n\n\n<p><strong>Effective increase or decrease = {(100 + x)\/100 * (100 + y)\/100 * (100 + z)\/100 \u2013 1} * 100%<\/strong><\/p>\n\n\n\n<p><strong>Example:<\/strong> A seller offers two successive discounts of 6.25% and 20% on a bag and is still able to earn 50% profit. If he offers only a single discount of 40% on M.R.P, what will be his profit percentage?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let C.P of bag = Rs. 100<\/p>\n\n\n\n<p>Then, S.P of bag = Rs. 150<\/p>\n\n\n\n<p>Let M.R.P of bag = Rs. x<\/p>\n\n\n\n<p>Effective discount = (-20) + (-6.25) + (-20)*(-6.25)\/100 = \u201325 (-ve sign indicates decrease)<\/p>\n\n\n\n<p>Effective discount percentage = 25%<\/p>\n\n\n\n<p>x*(100 \u2013 25)\/100=150<\/p>\n\n\n\n<p>x= Rs. 200<\/p>\n\n\n\n<p>New S.P = 200 * (100 \u2013 40)\/100 =Rs. 120<\/p>\n\n\n\n<p>Hence new profit = (120 \u2013 100)\/100 = 20%<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.oliveboard.in\/sbi-po\/?ref=contsp-sbi&amp;utm_medium=Organic&amp;utm_source=blog&amp;utm_campaign=contsp-sbi\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt Quant topic Tests for SBI PO Now to score more<\/a><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Constant amount of commodity in mixture<\/strong><\/h3>\n\n\n\n<p>For a commodity whose amount remains constant in a mixture<\/p>\n\n\n\n<p><strong>Quantity of new mixture * New % = Quantity of old mixture * Old %<\/strong><\/p>\n\n\n\n<p><strong>Example: <\/strong>An alcohol water mixture contains 14.28% alcohol. If 40 litres of water is added to the mixture, the new mixture contains 9.09% of alcohol. What was the quantity of initial mixture?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>14.28% = 1\/7 and 9.09% = 1\/11<\/p>\n\n\n\n<p>Let the initial quantity be y<\/p>\n\n\n\n<p>(y+40)*1\/11=y*1\/7<\/p>\n\n\n\n<p>y=70 litres<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Increase or decrease in consumption<\/strong><\/h3>\n\n\n\n<p>For expenditure to be constant when price increases\/decreases by r%<\/p>\n\n\n\n<p><strong>Increase or decrease in consumption =\u2502r\u2502\/(100 + r) * 100, \u2502r\u2502<\/strong><strong>\u2192<\/strong><strong>modulus of r<\/strong><\/p>\n\n\n\n<p><strong>Example: <\/strong>Price of sugar decreases by 20% then, by how much percentage the consumption should be increased so that expenditure remains constant?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Increase in consumption = \u2502(-20)\u2502\/(100 + (-20)) * 100 = 25% (-ve sign represents decrease)<\/p>\n\n\n\n<p>We hope this post helped you and gave some new tricks on how to solve percentage questions quickly as well as questions on ratios quickly. Practice more and more problems based on these tricks to get acquainted with it. All the best for your examination!<\/p>\n\n\n\n<p><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.oliveboard.prep\"><strong>Study at your own convenience anywhere. Download the Oliveboard app now!<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1664980729720\"><strong class=\"schema-faq-question\">How to solve<strong> successive increase or decrease<\/strong> questions ?<\/strong> <p class=\"schema-faq-answer\">Use the following formula : Effective increase or decrease = {(100 + x)\/100 * (100+y)\/100 \u2013 1} * 100% = x + y + (x*y)\/100. Check blog for detailed explanation.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1664980740809\"><strong class=\"schema-faq-question\">How to solve <strong>quantity in new mixture<\/strong> questions ?<\/strong> <p class=\"schema-faq-answer\">Use the formula : Quantity of new mixture * New % = Quantity of old mixture * Old %. For detailed explanation, read the blog above.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1664980742009\"><strong class=\"schema-faq-question\">What are shortcut formulas for percentage questions ?<\/strong> <p class=\"schema-faq-answer\">Check the blog above for important shortcut formulas for percentages<\/p> <\/div> <\/div>\n","protected":false},"excerpt":{"rendered":"<p>SBI PO and SSC CGL are around the corner. Percentages and ratios form the base for solving questions from many<\/p>\n","protected":false},"author":2,"featured_media":104750,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31,10224,10231,63,2],"tags":[],"class_list":["post-65257","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bank-exams","category-sbi","category-ssc-railways","category-ssc-exams","category-exam-hacks","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.6 (Yoast SEO v26.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Tips on how to solve questions on percentages and ratios quickly<\/title>\n<meta name=\"description\" content=\"In this blog, we will look at some useful tips on how to solve percentage questions quickly as well as questions on ratios.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.oliveboard.in\/blog\/how-to-solve-percentage-questions-quickly\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tips and tricks to solve questions on percentages and ratios quickly\" \/>\n<meta property=\"og:description\" content=\"SBI PO and SSC CGL are around the corner. 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