{"id":4218,"date":"2025-06-04T15:13:47","date_gmt":"2025-06-04T15:13:47","guid":{"rendered":"https:\/\/diznr.com\/?p=4218"},"modified":"2025-06-04T15:13:47","modified_gmt":"2025-06-04T15:13:47","slug":"mathematics-short-tricks-ratio-and-proportion","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/mathematics-short-tricks-ratio-and-proportion\/","title":{"rendered":"Mathematics Short Tricks\/Ratio and Proportion"},"content":{"rendered":"<p>Mathematics Short Tricks\/Ratio and Proportion<\/p>\n<p>[fvplayer id=&#8221;664&#8243;]<\/p>\n<p>\u092f\u0939\u093e\u0901 <strong>Ratio and Proportion (\u0905\u0928\u0941\u092a\u093e\u0924 \u0914\u0930 \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924)<\/strong> \u0915\u0947 \u0932\u093f\u090f \u0915\u0941\u091b \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 <strong>Maths Short Tricks<\/strong> \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902 \u091c\u094b \u092a\u094d\u0930\u0924\u093f\u092f\u094b\u0917\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e\u0913\u0902 (\u091c\u0948\u0938\u0947: GATE, SSC, Bank, UPSC, \u0906\u0926\u093f) \u092e\u0947\u0902 \u0924\u0947\u091c\u093c\u0940 \u0938\u0947 \u0938\u0935\u093e\u0932 \u0939\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0906\u092a\u0915\u0940 \u092e\u0926\u0926 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udcd8 <strong>1. \u0905\u0928\u0941\u092a\u093e\u0924 (Ratio) \u0915\u093e \u092e\u0942\u0932 \u091c\u094d\u091e\u093e\u0928<\/strong><\/h2>\n<p><strong>Definition:<\/strong><br \/>\n\u092f\u0926\u093f \u0926\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 a \u0914\u0930 b \u0939\u0948\u0902, \u0924\u094b \u0909\u0928\u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p><span class=\"katex\">Ratio=ab\u00a0\u092f\u093e\u00a0a:b\\text{Ratio} = \\frac{a}{b} \\text{ \u092f\u093e } a:b<\/span><\/p>\n<blockquote><p>\u26a0\ufe0f Ratio \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u090f\u0915 \u0939\u0940 \u0907\u0915\u093e\u0908 \u092e\u0947\u0902 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/p><\/blockquote>\n<hr \/>\n<h2>\ud83e\udde0 <strong>2. \u0905\u0928\u0941\u092a\u093e\u0924 \u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u0936\u0949\u0930\u094d\u091f \u091f\u094d\u0930\u093f\u0915\u094d\u0938<\/strong><\/h2>\n<h3>\ud83d\udd38 Trick 1: \u0926\u094b \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u091c\u094b\u0921\u093c\u0928\u093e<\/h3>\n<p>\u092f\u0926\u093f <span class=\"katex\">A:B=2:3A:B = 2:3<\/span> \u0914\u0930 <span class=\"katex\">B:C=4:5B:C = 4:5<\/span>, \u0924\u094b <span class=\"katex\">A:B:CA:B:C<\/span> \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f:<\/p>\n<p><strong>Step 1:<\/strong> B \u0915\u093e LCM \u0932\u094b \u2192 B = 3 \u0914\u0930 4 \u0915\u093e LCM = 12<br \/>\n\u0905\u092c A:B = 8:12 (2\u00d74 : 3\u00d74),<br \/>\n\u0914\u0930 B:C = 12:15 (4\u00d73 : 5\u00d73)<br \/>\n\u21d2 Final Ratio: A:B:C = <strong>8:12:15<\/strong><\/p>\n<hr \/>\n<h3>\ud83d\udd38 Trick 2: \u0915\u093f\u0938\u0940 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u094b \u092c\u0922\u093c\u093e\u0928\u093e \u092f\u093e \u0918\u091f\u093e\u0928\u093e<\/h3>\n<p><strong>Q:<\/strong> A \u0914\u0930 B \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 4:5 \u0939\u0948\u0964 \u0926\u094b\u0928\u094b\u0902 \u092e\u0947\u0902 \u20b9200 \u091c\u094b\u0921\u093c\u0928\u0947 \u092a\u0930 \u0928\u092f\u093e \u0905\u0928\u0941\u092a\u093e\u0924 5:6 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964 A \u0914\u0930 B \u0915\u0940 \u092e\u0942\u0932 \u0930\u093e\u0936\u093f \u0915\u094d\u092f\u093e \u0925\u0940?<\/p>\n<p><strong>Trick:<\/strong><br \/>\n\u092e\u093e\u0928 \u0932\u094b A = 4x, B = 5x<br \/>\n\u21d2 (4x + 200)\/(5x + 200) = 5\/6<br \/>\n\u0915\u094d\u0930\u0949\u0938 \u092e\u0932\u094d\u091f\u0940\u092a\u094d\u0932\u093e\u0908 \u0915\u0930\u0915\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u094b:<\/p>\n<p><span class=\"katex\">6(4x+200)=5(5x+200)\u21d224x+1200=25x+1000\u21d2x=2006(4x + 200) = 5(5x + 200) \\Rightarrow 24x + 1200 = 25x + 1000 \\Rightarrow x = 200<\/span><\/p>\n<p>\u21d2 A = 800, B = 1000<\/p>\n<hr \/>\n<h3>\ud83d\udd38 Trick 3: \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u092c\u0902\u091f\u0935\u093e\u0930\u093e<\/h3>\n<p><strong>Q:<\/strong> \u20b91800 \u0915\u094b 2:3:4 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u092c\u093e\u0902\u091f\u0928\u093e \u0939\u0948\u0964<\/p>\n<p><strong>Step:<\/strong><br \/>\nTotal Parts = 2+3+4 = 9<br \/>\n\u21d2 1 Part = 1800 \u00f7 9 = \u20b9200<br \/>\n\u21d2 Final Shares = 2\u00d7200 : 3\u00d7200 : 4\u00d7200 = \u20b9400, \u20b9600, \u20b9800<\/p>\n<hr \/>\n<h2>\ud83d\udd22 <strong>3. \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924 (Proportion)<\/strong><\/h2>\n<p><strong>Definition:<\/strong><br \/>\n\u091c\u092c \u0926\u094b \u0905\u0928\u0941\u092a\u093e\u0924 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902, \u091c\u0948\u0938\u0947:<\/p>\n<p><span class=\"katex\">ab=cd\u21d2a:b=c:d\u21d2a\u22c5d=b\u22c5c\\frac{a}{b} = \\frac{c}{d} \\Rightarrow a:b = c:d \\Rightarrow a \\cdot d = b \\cdot c<\/span><\/p>\n<p>\u0907\u0938\u092e\u0947\u0902 a \u0914\u0930 d \u0915\u094b <strong>extremes<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 b \u0914\u0930 c \u0915\u094b <strong>means<\/strong><\/p>\n<hr \/>\n<h2>\u26a1\ufe0f <strong>4. Golden Shortcut: Inverse Proportion<\/strong><\/h2>\n<p><strong>Q:<\/strong> \u092f\u0926\u093f \u0915\u093e\u0930\u094d\u092f A, B \u0914\u0930 C \u0915\u094d\u0930\u092e\u0936\u0903 3 \u0926\u093f\u0928, 6 \u0926\u093f\u0928 \u0914\u0930 9 \u0926\u093f\u0928 \u092e\u0947\u0902 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u093e\u092e \u0915\u094b \u092c\u0930\u093e\u092c\u0930 \u092c\u093e\u0901\u091f\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0948\u0938\u093e \u0915\u0948\u0938\u0947 \u092c\u093e\u0901\u091f\u093e \u091c\u093e\u090f?<\/p>\n<p><strong>Trick:<\/strong><br \/>\nTime \u221d 1\/Money<br \/>\n\u0924\u094b Ratio = 1\/3 : 1\/6 : 1\/9<br \/>\nLCM = 18<br \/>\n\u21d2 Ratio = 6:3:2<\/p>\n<hr \/>\n<h2>\ud83e\uddee <strong>5. Miscellaneous Important Ratios<\/strong><\/h2>\n<table>\n<thead>\n<tr>\n<th>Concept<\/th>\n<th>Shortcut \/ Ratio<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u092a\u0941\u0930\u0941\u0937 : \u0938\u094d\u0924\u094d\u0930\u0940 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924<\/td>\n<td>Always simplify both sides, like 5:3<\/td>\n<\/tr>\n<tr>\n<td>\u092e\u093f\u0936\u094d\u0930\u0923 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u093e\u0924<\/td>\n<td>Allegation Rule \u0938\u0947<\/td>\n<\/tr>\n<tr>\n<td>\u0932\u093e\u092d \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u093e\u0924<\/td>\n<td>C.P \u0914\u0930 S.P \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0928\u093f\u0915\u093e\u0932\u0947\u0902<\/td>\n<\/tr>\n<tr>\n<td>\u0938\u092e\u092f \u0914\u0930 \u0915\u093e\u0930\u094d\u092f<\/td>\n<td>Inverse ratio: \u0915\u093e\u0930\u094d\u092f \u221d 1\/\u0938\u092e\u092f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2>\ud83d\udccc Extra Tip:<\/h2>\n<h3>\u2705 Ratio Questions \u092e\u0947\u0902 \u0939\u092e\u0947\u0936\u093e:<\/h3>\n<ul>\n<li>\u0915\u092e \u0938\u0947 \u0915\u092e \u0930\u0942\u092a (lowest terms) \u092e\u0947\u0902 ratio \u0926\u094b<\/li>\n<li>\u090f\u0915\u0915 \u0938\u092e\u093e\u0928\u0924\u093e (unit matching) \u0915\u0940 \u091c\u093e\u0902\u091a \u0915\u0930\u094b<\/li>\n<li>Cross-multiplication \u092e\u0947\u0902 \u0917\u0932\u0924\u0940 \u0938\u0947 \u092c\u091a\u094b<\/li>\n<\/ul>\n<hr \/>\n<h2>\ud83c\udf81 PDF \/ Practice Set \u091a\u093e\u0939\u093f\u090f?<\/h2>\n<p>\u092e\u0948\u0902 \u0906\u092a\u0915\u094b Hindi \u092f\u093e English \u092e\u0947\u0902 Ratio and Proportion \u0915\u0940 PDF \u092d\u0940 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0915\u0947 \u0926\u0947 \u0938\u0915\u0924\u093e \u0939\u0942\u0901 (including tricks + practice questions)\u0964 \u092c\u0924\u093e\u0907\u090f \u0915\u094d\u092f\u093e \u091a\u093e\u0939\u093f\u090f?<\/p>\n<hr \/>\n<p>\u0906\u092a \u091a\u093e\u0939\u0947\u0902 \u0924\u094b \u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0917\u090f topics \u092a\u0930 \u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u092d\u0940 \u092e\u093e\u0902\u0917 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul>\n<li>Time and Work<\/li>\n<li>Speed, Time, and Distance<\/li>\n<li>Percentage<\/li>\n<li>Profit and Loss<\/li>\n<li>Mixture and Alligation<\/li>\n<\/ul>\n<p>\u092c\u0924\u093e\u0907\u090f \u0915\u094d\u092f\u093e \u0905\u0917\u0932\u093e \u091a\u093e\u0939\u093f\u090f?<\/p>\n<h3><a href=\"https:\/\/www.careerride.com\/Tips-tricks-and-formulae-on-Ratio-and-Proportion.pdf\" target=\"_blank\" rel=\"noopener\">Mathematics Short Tricks\/Ratio and Proportion<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/blogmedia.testbook.com\/blog\/wp-content\/uploads\/2021\/12\/maths-ratio-and-proportion-74674c04.pdf\" target=\"_blank\" rel=\"noopener\">Ratio and Proportion: Concepts, Solved Examples, &amp; &#8230;<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.jaipuria.ac.in\/blog\/wp-content\/uploads\/2023\/07\/Quant-Short-Tricks-PDF.pdf\" target=\"_blank\" rel=\"noopener\">QUALITATIVE APTITUDE TRICKS &amp; SHORTCUTS FOR<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Mathematics Short Tricks\/Ratio and Proportion [fvplayer id=&#8221;664&#8243;] \u092f\u0939\u093e\u0901 Ratio and Proportion (\u0905\u0928\u0941\u092a\u093e\u0924 \u0914\u0930 \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924) \u0915\u0947 \u0932\u093f\u090f \u0915\u0941\u091b \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 Maths Short Tricks \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902 \u091c\u094b \u092a\u094d\u0930\u0924\u093f\u092f\u094b\u0917\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e\u0913\u0902 (\u091c\u0948\u0938\u0947: GATE, SSC, Bank, UPSC, \u0906\u0926\u093f) \u092e\u0947\u0902 \u0924\u0947\u091c\u093c\u0940 \u0938\u0947 \u0938\u0935\u093e\u0932 \u0939\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0906\u092a\u0915\u0940 \u092e\u0926\u0926 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \ud83d\udcd8 1. \u0905\u0928\u0941\u092a\u093e\u0924 (Ratio) \u0915\u093e \u092e\u0942\u0932 \u091c\u094d\u091e\u093e\u0928 Definition: \u092f\u0926\u093f \u0926\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 a [&hellip;]<\/p>\n","protected":false},"author":64,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83],"tags":[],"class_list":["post-4218","post","type-post","status-publish","format-standard","hentry","category-mathematics-short-tricks"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/64"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=4218"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4218\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=4218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=4218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=4218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}