{"id":11257,"date":"2024-03-12T16:35:18","date_gmt":"2024-03-12T11:05:18","guid":{"rendered":"https:\/\/gstguntur.com\/?p=11257"},"modified":"2024-03-13T17:50:52","modified_gmt":"2024-03-13T12:20:52","slug":"ratio-and-proportion-ca-foundation-maths-study-material","status":"publish","type":"post","link":"https:\/\/gstguntur.com\/ratio-and-proportion-ca-foundation-maths-study-material\/","title":{"rendered":"Ratio and Proportion \u2013 CA Foundation Maths Study Material"},"content":{"rendered":"<p>This Ratio and Proportion \u2013 <a href=\"https:\/\/gstguntur.com\/ca-foundation-maths-chapter-wise-questions\/\">CA Foundation Maths Study Material<\/a>\u00a0is designed strictly as per the latest syllabus and exam pattern.<\/p>\n<h2>Ratio and Proportion \u2013 CA Foundation Maths Study Material<\/h2>\n<p><strong>Ratio:<\/strong><br \/>\nThe comparison of two or more things of same kind is called Ratio. If x and y are two values of same kind (in same units), then the ratio of x to y is written as x : y and read as x is to y.<br \/>\nIn \\(\\frac{x}{y}\\)<\/p>\n<ul>\n<li>Numerator \u201cx\u201d is called 1st term or Antecedent and<\/li>\n<li>Denominator \u201cy\u201d is called 2nd term or Consequent.<\/li>\n<li>Antecedent and Consequent must be of same units<\/li>\n<li>Ratio has no unit.<\/li>\n<\/ul>\n<p>Remarks:<\/p>\n<ul>\n<li>Normally a ratio is expressed in simplest form. As. 10:16 = 5:8.<\/li>\n<li>The order of the terms in a ratio must be maintained. As 3 : 4 is not same as 4:<\/li>\n<li>Ratio exists only with quantities having same unit (kind).\n<ul>\n<li>If x &gt; y, then the ratio x : y is called of greater inequality.<\/li>\n<li>If x &lt; y, then the ratio x : y is called of lesser inequality.<\/li>\n<li>If x = y, then the ratio a : b is called ratio of Equal Equality.<\/li>\n<li>Duplicate ratio of a : b is a<sup>2<\/sup>: b<sup>2<\/sup><\/li>\n<li>Triplicate ratio of a : b is a<sup>3<\/sup> : b<sup>3<\/sup><\/li>\n<li>Sub-Duplicate ratio of a : b is \u221aa : \u221ab = a<sup>1\/2<\/sup> : b<sup>1\/2<\/sup><\/li>\n<li>Sub-Triplicate ratio of a : b is 3\u221aa ; 3\u221ab = a<sup>1\/3<\/sup> : b<sup>1\/3<\/sup><\/li>\n<\/ul>\n<\/li>\n<li>Inverse ratio of x : y is y : x.\n<ul>\n<li>Commensurable: If the terms of the ratio are integers, the ratio is called commensurable. As. 3 :2<\/li>\n<li>Incommensurable : If the terms of the ratio are not integers, the ratio is called Incommensurable.<br \/>\nAs \u221a3 : \u221a2 cannot be expressed in terms of integers. So, it is Incom-mensurable.<\/li>\n<\/ul>\n<\/li>\n<li>Compound\/Combined Ratio = Product of all ratios.<\/li>\n<\/ul>\n<p><strong>Proportion:<\/strong><br \/>\nAn equality of two ratios is called Proportion. Four quantities a, b, c, d are said to be in proportion if a : b = c : d.<br \/>\nIt is also written as<br \/>\na : b : : c : d<br \/>\nHere a, b, c, d are called 1st; 2nd; 3rd and 4th term of proportionals respectively a c<br \/>\nIf \\(\\frac{a}{b}=\\frac{c}{d}\\) \u21d2 ad = bc.<br \/>\nProduct of extreme terms = Product of middle terms.<br \/>\nThis rule is called Cross &#8211; Product Rule.<\/p>\n<p>In a: b :: c : d. proportion, unit of a and b should be same and that of c and d should also be same.<br \/>\nAs. \u20b9 6 : \u20b9 8 = 12 toffees : 16 toffees are in proportion.<br \/>\nLet a, b and c are of same kind (in same units). a b<br \/>\nIf \\(\\frac{a}{b}=\\frac{b}{c}\\) \u21d2 a : b : : b : c<br \/>\ni. e. a, b, c are in proportion. &#8216;<br \/>\nThen, this proportion is called continuous proportion.<br \/>\nHere a is 1st proportion c is called 3rd proportion and b is called mean proportion.<br \/>\nb = \\(\\sqrt{a c}\\) = GM of a &amp; c.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p><strong>Properties of Proportion<\/strong><br \/>\n1. Cross-Product<br \/>\nIf a : b : : c : d.<br \/>\n\u21d2 \\(\\frac{a}{b}=\\frac{c}{d}\\) \u2234 ad = be.<\/p>\n<p>2. Invertendo<br \/>\nIf a : b : : c : d.; Then its inverse<br \/>\nb : a :: d : c also becomes in proportion.<br \/>\ni.e. If \\(\\frac{a}{b}=\\frac{c}{d}\\) Then, \\(\\frac{b}{a}=\\frac{d}{c}\\)<\/p>\n<p>3. Componendo<br \/>\nIf a : b :: c : d.<br \/>\nThen a + b:b::c + d:d.<br \/>\nProof \\(\\frac{a}{b}+1=\\frac{c}{d}+1 \\Rightarrow \\frac{a+b}{b}=\\frac{c+d}{d}\\)<\/p>\n<p>4. Dividendo<br \/>\nIf a : b = c : d.<br \/>\nThen a &#8211; b : b = c &#8211; d : d.<br \/>\nProof: \\(\\frac{a}{b}=\\frac{c}{d} \\Rightarrow \\frac{a}{b}-1=\\frac{c}{d}-1\\)<br \/>\nor \\(\\frac{a-b}{b}=\\frac{c-d}{d}\\)<\/p>\n<p>5. Componendo and Dividendo<br \/>\nIf a : b : : c : d. ; Dividing (3) by (4)<br \/>\nThen, \\(\\frac{a+b}{a-b}=\\frac{c+d}{c-d}\\)<\/p>\n<p>6. Alternendo:<br \/>\nIf a : b : : c : d<br \/>\nThen a : c : : b : d<br \/>\ni.e ratio of alternate terms are also in proportion.<\/p>\n<p>7. Addendo<br \/>\nIf a : b = c : d = e : f = &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;<br \/>\nThen each ratio = \\(\\frac{\\text { Sum of antecedents of all ratios }}{\\text { Sum of consequents of all ratios }}\\)<br \/>\n\u2234 \\(\\frac{a}{b}=\\frac{c}{d}=\\frac{e}{f}=\\ldots \\ldots \\ldots .=\\frac{a+c+e+\\ldots \\ldots}{b+d+f+\\ldots}\\)<\/p>\n<p>8. Subtrahendo<br \/>\nIf \\(\\frac{a}{b}=\\frac{c}{d}=\\frac{e}{f}\\) = &#8230;&#8230;&#8230;.<br \/>\nThen each ratio<br \/>\n\u2234 \\(=\\frac{a}{b}=\\frac{c}{d}=\\frac{e}{f}=\\ldots \\ldots \\ldots .=\\frac{a-c-e-\\ldots .}{b-d-f-\\ldots .}\\)<\/p>\n<p><strong>Previous Year Exam Questions<\/strong><\/p>\n<p>Question 1.<br \/>\nTwo numbers are in the ratio of 2 : 3 and the difference of their squares is 320. The number are : [1 Mark, Nov. 2006]<br \/>\n(a) 12, 18<br \/>\n(b) 16, 24<br \/>\n(c) 14, 21<br \/>\n(d) None<br \/>\nAnswer:<br \/>\nTricks : Go by choices (a); (b) &amp; (c) all are in ratio 2:3 But For option<br \/>\n(a) 18<sup>2<\/sup> &#8211; 12<sup>2<\/sup> \u2260 320<br \/>\n(b) 24<sup>2<\/sup> &#8211; 16<sup>2<\/sup> = (24+ 16) (24 &#8211; 16)<br \/>\n= 40 \u00d7 8 = 320<\/p>\n<p>Question 2.<br \/>\nIf p : q is the sub-duplicate ratio of p &#8211; x<sup>2<\/sup>: q &#8211; x<sup>2<\/sup>, then x<sup>2<\/sup> is : [1 Mark, Nov. 2006]<br \/>\n(a) \\(\\frac{p}{p+q}\\)<br \/>\n(b) \\(\\frac{q}{p+q}\\)<br \/>\n(c) \\(\\frac{q p}{p-q}\\)<br \/>\n(d) None<br \/>\nAnswer:<br \/>\nDetail Method:<br \/>\n\\(\\frac{\\sqrt{p-x^2}}{\\sqrt{q-x^2}}=\\frac{p}{q}\\)<br \/>\nSquaring on both side; we get<br \/>\n\\(\\frac{p-x^2}{q-x^2}=\\frac{p^2}{q^2}\\)<br \/>\nor pq<sup>2<\/sup> &#8211; q<sup>2<\/sup>x<sup>2<\/sup> = p<sup>2<\/sup>q &#8211; p<sup>2<\/sup>x<sup>2<\/sup><br \/>\nor p<sup>2<\/sup>x<sup>2<\/sup> &#8211; q<sup>2<\/sup>x<sup>2<\/sup> = p<sup>2<\/sup>q &#8211; pq<sup>2<\/sup><br \/>\nor x<sup>2<\/sup>(p<sup>2<\/sup> &#8211; q<sup>2<\/sup>) = pq(p &#8211; q)<br \/>\nor x<sup>2<\/sup> (p + q)(p-q) = pq (p &#8211; q)<br \/>\n(d) is correct<br \/>\nTricks : Go by choices.<\/p>\n<p>Question 3.<br \/>\nAn alloy is to contain copper and zinc in the ratio 9:4. The zinc required to melt with 24 kg of copper is : [1 Mark, Nov. 2006]<br \/>\n(a) 10\\(\\frac{2}{3}\\)kg<br \/>\n(b) 10\\(\\frac{1}{3}\\)kg<br \/>\n(c) 9\\(\\frac{2}{3}\\)kg<br \/>\n(d) 9 kg<br \/>\nAnswer:<br \/>\nLet Zinc = x kg<br \/>\n(a) \u2234 \\(\\frac{9}{4}=\\frac{24}{x}\\) \u2234 x = \\(\\frac{4 \\times 24}{9}=\\frac{32}{3}\\)<br \/>\n= 10\\(\\frac{2}{3}\\)kg<br \/>\n\u2234 (a) is correct<\/p>\n<p>Question 4.<br \/>\nTwo numbers are in the ratio 7: 8. If 3 is added to each of them, their ratio becomes 8 : 9. The numbers are: [1 Mark, Feb. 2007]<br \/>\n(a) 14,16<br \/>\n(b) 24,27<br \/>\n(c) 21,24<br \/>\n(d) 16,18<br \/>\nAnswer:<br \/>\nTricks : Go by choices<br \/>\n(b) and (d) are not in the ratio 7 : 8 So (b) &amp; (d) are not answer For (a) it is added then<br \/>\n\\(\\frac{14+3}{10+3}=\\frac{17}{19} \\neq \\frac{8}{9}\\)<br \/>\n(a) is not answer<br \/>\n(c) is answer Detail Method:<br \/>\nLet x is common in the ratio<br \/>\n\u2234 Numbers are 7x &amp; 8x<br \/>\nNow \\(\\frac{7 x+3}{8 x+3}=\\frac{8}{9}\\)<br \/>\nor 64x + 24 = 63x + 27<br \/>\nor 64x &#8211; 63x = 27-24<br \/>\nor x = 3<br \/>\n1st number = ix = 7&#215;3 = 21<br \/>\n2nd number = 8x = 8&#215;3 = 24<br \/>\n(c) is correct<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p>Question 5.<br \/>\nA box contains \u20b9 56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The numbers of 50 paise coins in the box is : [1 Mark, Feb. 2007]<br \/>\n(a) 64<br \/>\n(b) 32<br \/>\n(c) 16<br \/>\n(d) 14<br \/>\nAnswer:<br \/>\nTricks : Go by choices<br \/>\nNo. of 25 paise coins = \\(\\frac{1}{2}\\) No. of 50 Paise<br \/>\nNo. of Rupee coins = \\(\\frac{1}{4}\\) No. of 50 Paise Coins<br \/>\nFor (a) No. of coins of \u20b9 1;50 Paise &amp; 25 Paise<br \/>\n\\(\\frac{64}{4}\\); 64; \\(\\frac{64}{2}\\)<br \/>\nTotal Value = 16 \u00d7 1 + 64 \u00d7 0.50 + 32 \u00d7 0.25<br \/>\n= \u20b9 16 + 32 + 8 = \u20b9 56<br \/>\nWhich is equal to given value (a) is Correct<\/p>\n<p>Detail Method<br \/>\nLet No. of 50 Paise coins = x<br \/>\n\u2234 No. of \u20b9 1 coins = \\(\\frac{x}{4}\\)<br \/>\nand No. of 25 Paise coins = \\(\\frac{x}{2}\\)<br \/>\n\u2234 Total Value =<br \/>\n\\(\\frac{x}{4}\\) \u00d7 1 + x \u00d7 0.50+ \\(\\frac{x}{2}\\) \u00d7 0.25 = 56<br \/>\nor 0.25x + 0.50x + 0.125x<br \/>\nor 0.875x = 56<br \/>\nor x = \\(\\frac{56}{0.875}\\) = 64<br \/>\n\u2234 (a) is correct<\/p>\n<p>Question 6.<br \/>\nEight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally entire cost of the car, then the share of each of the remaining persons increased by : [1 Mark, May 2007]<br \/>\n(a) 1\/9<br \/>\n(b) 1\/8<br \/>\n(c) 1\/7<br \/>\n(d) 7\/8<br \/>\nAnswer:<br \/>\nTricks : Per Person share increase = \\(\\frac{1}{7}\\) of total share<\/p>\n<p>Question 7.<br \/>\nA bag contains \u20b9 187 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio 3:4:5. Find the number of each type of coins: [1 Mark, May 2007]<br \/>\n(a) 102, 136, 170<br \/>\n(b) 136, 102, 170<br \/>\n(c) 170, 102, 136<br \/>\n(d) None<br \/>\nAnswer:<br \/>\nTricks I: Go by choices<br \/>\nFor (a) Coins are in the ratio 3:4:5<br \/>\n\u2234 \\(\\frac{102}{3}=\\frac{136}{4}=\\frac{170}{5}\\) = 34<br \/>\nIt satisfies 1st condition<br \/>\nNow 102 \u00d7 1 + 136 \u00d7 0.50 + 170 \u00d7 0.10<br \/>\n= 102 + 68 + 17 = \u20b9 187<br \/>\n\u2234 (a) is correct<br \/>\nTricks II<br \/>\nCommon factor = \\(\\frac{187}{3 \\times 1+4 \\times 0.50+5 \\times 0.10}\\)<br \/>\n= \\(\\frac{187}{5.50}\\) = 34<br \/>\n\u2234 No. of 1 Rupee coins =3 \u00d7 34 = 102<br \/>\nNo. of 50 Paise coins =4 \u00d7 34 = 136<br \/>\nNo. of 10 paise coins = 5 \u00d7 34 = 170 (a) is correct<\/p>\n<p>Detail Method<br \/>\nLet x is common in the ratio<br \/>\nNo. of 1 Rupee ; 50 Paise and 10 Paise Coins are 3x ; 4x and 5x<br \/>\n\u2234 3x \u00d7 1 + 4x \u00d7 0.50 + 5x \u00d7 0.10 = 187<br \/>\nor 5.50x = 187<br \/>\n\u2234 x = \\(\\frac{187}{5.50}\\) = 34<br \/>\n\u2234 No. of 1 Rupee coins = 3x = 3 \u00d7 34 = 102<br \/>\nNo. of 50 Paise coins = 4x = 4 \u00d7 34 = 136<br \/>\nNo. of 10 Paise coins = 5x = 5 \u00d7 34 = 170<br \/>\n\u2234 (a) is correct<\/p>\n<p>Question 8.<br \/>\nRatio of earnings of A and B is 4 : 7. If the earnings of A increase by 50% and those of B decrease by 25%, the new ratio of their earning becomes 8 : 7. What is A\u2019s earning ?<br \/>\n(a) \u20b9 21,000<br \/>\n(b) \u20b9 26,000<br \/>\n(c) \u20b9 28,000<br \/>\n(d) Data inadequate [1 Mark, Aug. 2007]<br \/>\nAnswer:<br \/>\nDetailed Method Let x is common in the ratio<br \/>\n\u2234 A\u2019s and B\u2019s present earnings are 4x and 7x respectively<br \/>\nFrom question \\(\\frac{4 x+4 x \\times 0.50}{7 x-7 x \\times 0.25}=\\frac{8}{7}\\)<br \/>\nor \\(\\frac{6 x}{5.25 x}=\\frac{8}{7}\\)<br \/>\nx cannot be found.<br \/>\nData is inadequate<br \/>\n\u2234 (d) is Correct<\/p>\n<p>Question 9.<br \/>\nP, Q and R are three cities. The ratio of average temperature between P and Q is 11 : 12 and that of between P and R is 9: 8. The ratio between the average temperature of Q and R is : [1 Mark, Aug. 2007]<br \/>\n(a) 22: 27<br \/>\n(b) 27: 22<br \/>\n(c) 32: 33<br \/>\n(d) None<br \/>\nAnswer:<br \/>\n\u2234 P: Q= 11 : 12 \u2234 Q :P= 12 : 11<br \/>\n\\(\\frac{Q}{P} \\times \\frac{P}{R}=\\frac{12}{11} \\times \\frac{9}{8}\\)<br \/>\n\\(\\frac{Q}{R}=\\frac{27}{22}\\) Q :P= 12 : 11<br \/>\n(b) is Correct<\/p>\n<p>Question 10.<br \/>\n\u20b9 407 are to be divided among A, B and C so that their shares are in the ratio \\(\\frac{1}{4}: \\frac{1}{5}: \\frac{1}{6}\\)<br \/>\nThe respective shares of A, B, C are: [1 Mark, Nov. 2007]<br \/>\n(a) \u20b9 165, \u20b9 132, \u20b9 110<br \/>\n(b) \u20b9 165, \u20b9 110, \u20b9 132<br \/>\n(c) \u20b9 132, \u20b9 110, \u20b9 165<br \/>\n(d) \u20b9 110, \u20b9 132, \u20b9 165.<br \/>\nAnswer:<br \/>\nA:B:C = \\(\\frac{1}{4}: \\frac{1}{5}: \\frac{1}{6}\\) \u00d7 LCM of denominators = 60<br \/>\n= 15 : 12 : 10<br \/>\n\u2234 A&#8217;s share = \\(\\frac{407}{15+12+10}\\) \u00d7 15 = Rs. 165<br \/>\nB\u2019s share = \\(\\frac{407}{37}\\) \u00d7 12 = Rs. 132<br \/>\nC\u2019s share = \\(\\frac{407}{37}\\)\u00d7 10 = Rs. 110<br \/>\n(a) is Correct<br \/>\nTricks : Go by Choices.<\/p>\n<p>Question 11.<br \/>\nThe incomes of A and B are in the ratio 3 :2 and their expenditures in the ratio 5 : 3. If each saves \u20b9 1,500, then B\u2019s income is : [1 Mark, Nov. 2007]<br \/>\n(a) \u20b9 6,000<br \/>\n(b) \u20b9 4,500<br \/>\n(c) \u20b9 3,000<br \/>\n(d) \u20b9 7,500<br \/>\nAnswer:<br \/>\nDetail Method Let x is common in the ratio.<br \/>\nA\u2019s income = 3x<br \/>\nB\u2019s income = 2x<br \/>\n\u2234 \\(\\frac{3 x-1500}{2 x-1500}=\\frac{5}{3}\\)<br \/>\nor 10x &#8211; 7500 = 9x &#8211; 4500<br \/>\nor 10x &#8211; 9x = 7500 &#8211; 4500<br \/>\nor x = 3000<br \/>\nB\u2019s income = 2x =2 \u00d7 3000<br \/>\n= \u20b9 6000.<br \/>\n(a) is Correct Tricks : Go by choices For (a)<br \/>\n\\(\\frac{A}{B}\\) Expenditure = \\(\\frac{\\frac{6000}{2} \\times 3-1500}{6000-1500}=\\frac{7500}{4500}=\\frac{5}{3}\\)<br \/>\n(a) is Correct<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p>Question 12.<br \/>\nIn 40 litres mixture of glycerine and water, the ratio of glycerine and water is 3:1. The quantity of water added in the mixture in order to make this ratio 2:1 is : [1 Mark, Feb. 2008 ]<br \/>\n(a) 15 litres<br \/>\n(b) 10 litres<br \/>\n(c) 8 litres<br \/>\n(d) 5 litres<br \/>\nAnswer:<br \/>\nGlycerine = \\(\\frac{40}{3+1}\\) x 3 = 30 litres.<br \/>\nWater = \\(\\frac{40}{4}\\) x 1 = 10 litres 4<br \/>\nLet x litres of water is added to the mixture<br \/>\nThen \\(\\frac{30}{10+x}=\\frac{2}{1}\\)<br \/>\nor, 2x + 20 = 30<br \/>\nor x = 5<br \/>\n\u2234 (d) is Correct<br \/>\nTricks : Go by Choices<\/p>\n<p>Question 13.<br \/>\nThe third proportional between (a<sup>2<\/sup> &#8211; b<sup>2<\/sup>) and (a + b)<sup>2<\/sup> is : [1 Mark, Feb. 2008]<br \/>\n(a) \\(\\frac{a+b}{a-b}\\)<br \/>\n(b) \\(\\frac{a-b}{a+b}\\)<br \/>\n(c) \\(\\frac{(a-b)^2}{a+b}\\)<br \/>\n(d) \\(\\frac{(a+b)^3}{a-b}\\)<br \/>\nAnswer:<br \/>\n3rd Proportion = \\(\\frac{(\\text { Mean prop. })^2}{\\text { lst Proportional }}\\)<br \/>\n= \\(\\frac{\\left\\{(a+b)^2\\right\\}^2}{a^2-b^2}=\\frac{(a+b)^4}{3(a+b)(a+b)}=\\frac{(a+b)^3}{a-b}\\)<br \/>\n(d) is Correct<\/p>\n<p>Question 14.<br \/>\nIn what ratio should tea worth \u20b9 10 per kg. be mixed with tea worth \u20b9 14 per kg., so that the average price of the mixture may be \u20b9 11 per kg.? [1 Mark, June 2008]<br \/>\n(a) 2 : 1<br \/>\n(b) 3 : 1<br \/>\n(c) 3 : 2<br \/>\n(d) 4 : 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-11585\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2023\/02\/Ratio-and-Proportion-\u2013-CA-Foundation-Maths-Study-Material-1.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material 1\" width=\"224\" height=\"164\" \/><br \/>\n\u2234 (b) is Correct<\/p>\n<p>Question 15.<br \/>\nThe ages of two persons are in the ratio 5:7. Eighteen years ago their ages were in the ratio of 8:13, their present ages (in years) are : [1 Mark, June 2008]<br \/>\n(a) 50; 70<br \/>\n(b) 70,50<br \/>\n(c) 40,56<br \/>\n(d) None<br \/>\nAnswer:<br \/>\nTricks : Go by choices (a) &amp; (c) are in the ratio 5 : 7 not (b)<br \/>\nFor (a) 18 year ago<br \/>\nSo, (a) is Correct<\/p>\n<p>Question 16.<br \/>\nIf A, B and C started a business by investing \u20b9 1,26,000, \u20b9 84,000 and \u20b9 2,10,000. If at the end of the year profit is \u20b9 2,42,000 then the share of each is : [1 Mark, Dec. 2008]<br \/>\n(a) \u20b9 72,600; \u20b9 48,400 ; \u20b9 1,21,000<br \/>\n(b) \u20b9 48,400 ; \u20b9 1,21,000 ; \u20b9 72,600<br \/>\n(c) \u20b9 72,000 ; \u20b9 49,000 ; \u20b9 1,21,000<br \/>\n(d) \u20b9 48,000 ; \u20b9 1,21,400 ; \u20b9 72,600<br \/>\nAnswer:<br \/>\nInvestment ratio is<br \/>\nA : B : C = 126,000 : 84,000 : 2,10,000 \u00f7 14,000<br \/>\n= 9: 6 : 15 \u00f7 3<br \/>\n= 3: 2: 5<br \/>\nA\u2019s share = \\(\\frac{\u20b9 242,000}{3+2+5}\\) \u00d7 3 =\u20b9 72, 600<br \/>\nB\u2019s share = \\(\\frac{242,000}{20}\\) \u00d7 2 = \u20b948, 400<br \/>\nC\u2019s share = \\(\\frac{242000}{10}\\) \u00d7 5 = \u20b9 1,21,000<br \/>\nSo, (a) is Correct<\/p>\n<p>Question 17.<br \/>\nIf \\(\\frac{p}{q}=-\\frac{2}{3}\\) then the value of \\(\\frac{2 p+q}{2 p-q}\\) is: [1 Mark, June 2009]<br \/>\n(a) 1<br \/>\n(b) \\(-\\frac{1}{7}\\)<br \/>\n(c) \\(\\frac{1}{7}\\)<br \/>\n(d) 7<br \/>\nAnswer:<br \/>\n\u2235 \\(\\frac{p}{q}=\\frac{-2}{3}\\)<br \/>\nTricks<br \/>\n\\(\\frac{2 p+q}{20-q}=\\frac{2(-2)+3}{2(-2)-3}=\\frac{-4+3}{-4-3}=\\frac{-1}{-7}=\\frac{1}{7}\\)<br \/>\n(c) is correct<\/p>\n<p>Question 18.<br \/>\nFourth proportional to x, 2x, (x +1) is :<br \/>\n(a) x + 2<br \/>\n(b) (x + 2)<br \/>\n(c) (2x + 2)<br \/>\n(d) (2x &#8211; 2)<br \/>\nAnswer:<br \/>\nLet Fourth Proportional is K.<br \/>\n\u2234 \\(\\frac{x}{2 x}=\\frac{x+1}{K}\\)<br \/>\nor k.x = 2x (x + 1)<br \/>\nor k = 2 (x + 1) = 2x +2<br \/>\n(c) is correct<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p>Question 19.<br \/>\nWhat must be added to each term of the ratio 49 : 68 so that it becomes 3 : 4? [1 Mark, June 2010]<br \/>\n(a) 3<br \/>\n(b) 5<br \/>\n(c) 8<br \/>\n(d) 9<br \/>\nAnswer:<br \/>\nDetail Method:<br \/>\nLet x is added to each term<br \/>\nThen \\(\\frac{49+x}{68+x}=\\frac{3}{4}\\)<br \/>\nor 196 +4x = 204 + 3x<br \/>\nor 4x &#8211; 3x = 204 &#8211; 196<br \/>\nor x = 8<br \/>\n(c) is Correct<br \/>\nTricks : Go by Choices<br \/>\n1st Find \\(\\frac{3}{4}\\) = 0.75 (By Calculator)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-11584\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2023\/02\/Ratio-and-Proportion-\u2013-CA-Foundation-Maths-Study-Material-2.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material 2\" width=\"248\" height=\"171\" \/><\/p>\n<p>Question 20.<br \/>\nThe students of two classes are in the ratios 5 : 7, if 10 students left from each class, the remaining students are in the ratio of 4 : 6, then the number of students in each class was : [1 Mark, June 2010]<br \/>\n(a) 30, 40<br \/>\n(b) 25, 24<br \/>\n(c) 40, 60<br \/>\n(d) 50, 70<br \/>\nAnswer:<br \/>\nTricks : Go by choices:<br \/>\n(a); (b) and (c) are not in the ratio 5 : 7<br \/>\n\u2234 (d) is Correct.<\/p>\n<p>Question 21.<br \/>\nIf A: B= 2: 5, then (10A + 3B) : (5A + 2B) is equal to: [1 Mark, Dec. 2010]<br \/>\n(a) 7: 4<br \/>\n(b) 7: 3<br \/>\n(c) 6: 5<br \/>\n(d) 7: 9<br \/>\nAnswer:<br \/>\nIt A : B = 2 : 5 Then<br \/>\n\\(\\frac{10 A+3 B}{5 A+2 B}=\\frac{10 \\times 2+3 \\times 5}{5 \\times 2+2 \\times 5}=\\frac{35}{20}=\\frac{7}{4}\\)<br \/>\n= 7: 4<br \/>\n(a) is Correct<\/p>\n<p>Question 22.<br \/>\nIn a film shooting, A and B received money in a certain ratio and B and C also received the money in the same ratio. If A gets \u20b9 1,60,000 and C gets \u20b9 2,50,000. Find the amount received by B ? [1 Mark, June 2011]<br \/>\n(a) \u20b9 2,00,000<br \/>\n(b) \u20b9 2,50,000<br \/>\n(c) \u20b9 1,00,000<br \/>\n(d) \u20b9 1,50,000<br \/>\nAnswer:<br \/>\nDetail Method<br \/>\nA : B = B : C<br \/>\nSo, B<sup>2<\/sup> = AC ;<br \/>\nso, B = \\(\\sqrt{\\mathrm{AC}}=\\sqrt{1,60,000 \\times 2,50,000}\\)<br \/>\n= 400 \u00d7 500 = 2,00,000<\/p>\n<p>Question 23.<br \/>\nThe ratio compounded of 4:5 and sub-duplicate of \u201c a\u201d : 9 is 8:15. Then value of \u201ca\u201d is: [1 Mark, Dec. 2011]<br \/>\n(a) 2<br \/>\n(b) 3<br \/>\n(c) 4<br \/>\n(d) 5<br \/>\nAnswer:<br \/>\n(c) \\(\\frac{4}{5} \\times \\sqrt{\\frac{a}{9}}=\\frac{8}{15}\\)<br \/>\nor \\(\\frac{4}{5} \\times \\frac{\\sqrt{a}}{3}=\\frac{8}{15}\\)<br \/>\n\u2234 \u221aa = 2 \u21d2 a = 4<br \/>\n(c) is Correct<\/p>\n<p>Question 24.<br \/>\nIf X varies inversely as square of Y and given that Y=2 for X = 1, then the value of X for Y =6 will be: [1 Mark, Dec. 2011]<br \/>\n(a) 3<br \/>\n(b) 9<br \/>\n(c) 1\/3<br \/>\n(d) 6<br \/>\nAnswer:<br \/>\n(d) is Correct<br \/>\nx \u00d7 \\(\\frac{1}{y^2}\\) \u21d2 x = K.\\(\\frac{1}{y^2}\\) x = \\(\\frac{k}{y^2}\\), where k = proportional constant<br \/>\nwhere k = proportional constant<br \/>\nWhen x = 1 Then y = 2<br \/>\n1 = \\(\\frac{k}{2^2}\\) \u21d2 k = 4 \u2234 x = \\(\\frac{4}{y^2}\\)<br \/>\nWhen y = 6, Then x = \\(\\frac{4}{6^2}=\\frac{1}{9}\\)<br \/>\nx = \\(\\frac{1}{9}\\)<\/p>\n<p>Question 25.<br \/>\nWhich of the numbers are not in proportion ?<br \/>\n(a) 6, 8, 5, 7<br \/>\n(b) 7, 14, 6, 12<br \/>\n(c) 18, 27,12, 18<br \/>\n(d) 8, 6, 12, 9<br \/>\nAnswer:<br \/>\n(a) Go by choices<br \/>\nFor (a) \\(\\frac{6}{8}=\\frac{3}{4} \\neq \\frac{5}{7}\\)<br \/>\n(a) is not in proportion<\/p>\n<p>Question 26.<br \/>\nFind two numbers such that mean proportional between them is 18 and third proportional between them is 144: [1 Mark, Dec. 2012]<br \/>\n(a) 9 ; 36<br \/>\n(b) 8 ; 32<br \/>\n(c) 7 ; 28<br \/>\n(d) 6 ; 14<br \/>\nAnswer:<br \/>\n(a) is correct Tricks : Go by choices<br \/>\nFor (a) Mean Proportional of 9 and 36<br \/>\n= \\(\\sqrt{9 \\times 36}\\) = 18<br \/>\nIt satisfies 1st condition.<br \/>\nIf 144 is its 3rd condition.<br \/>\n36<sup>2<\/sup> = 9 \u00d7 144<br \/>\nIt also satisfies the 2nd Condition.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p>Question 27.<br \/>\nTriplicate ratio of 4 : 5 is: [1 Mark, June 2013]<br \/>\n(a) 125 : 64<br \/>\n(b) 16 : 25<br \/>\n(c) 64 : 125<br \/>\n(d) 120 : 46<br \/>\nAnswer:<br \/>\n(c) Triplicate ratio of 4:5 = 4<sup>3<\/sup> :5<sup>3<\/sup> = 64: 125<\/p>\n<p>Question 28.<br \/>\nThe mean proportion between 24 and 54 is _______. [1 Mark, June 2013]<br \/>\n(a) 33<br \/>\n(b) 34<br \/>\n(c) 35<br \/>\n(d) 36<br \/>\nAnswer:<br \/>\n(d) Mean &#8211; Proportion = \\(\\sqrt{24 \\times 54}\\) = 36<\/p>\n<p>Question 29.<br \/>\nThe ratio of numbers is 1:2:3 and sum of their squares is 504 then the numbers are: [1 Mark, Dec. 2013]<br \/>\n(a) 6, 12, 18<br \/>\n(b) 3, 6, 9<br \/>\n(c) 4, 8, 12<br \/>\n(d) 5, 10, 15<br \/>\nAnswer:<br \/>\n(a) is correct<br \/>\nTricks : Go by choices<br \/>\nTricks : See Quicker BMLRS<\/p>\n<p>Question 30.<br \/>\nIf P is 25% less than Q and R is 20% higher than Q the Ratio of R and P: [1 Mark, Dec. 2013]<br \/>\n(a) 5:8<br \/>\n(b) 8:5<br \/>\n(c) 5:3<br \/>\n(d) 3:5<br \/>\nAnswer:<br \/>\n(b) is correct<br \/>\nLet Q = 100, So, P = 100 &#8211; 025 = 75<br \/>\n&amp;R = 100 + 20= 120<br \/>\n\\(\\frac{R}{P}=\\frac{120}{75}=\\frac{8}{5}\\)<\/p>\n<p>Question 31.<br \/>\nA person has assets worth \u20b9 1,48,200. He wish to divide it amongst his wife, son and daughter in the ratio 3:2:1 respectively. From this assets the share of his son will be: [1 Mark, June 2014]<br \/>\n(a) \u20b9 74,100<br \/>\n(b) \u20b9 37,050<br \/>\n(c) \u20b9 49,400<br \/>\n(d) \u20b9 24, 700<br \/>\nAnswer:<br \/>\n(c) is correct<br \/>\nShare of son = \\(\\frac{2}{3+2+1}\\) \u00d7 1,48,200<br \/>\n= \u20b9 49,400<\/p>\n<p>Question 32.<br \/>\nIf x : y = 2 : 3 then (5x+2y): (3x -y) = [1 Mark, June 2014]<br \/>\n(a) 19 : 3<br \/>\n(b) 16: 3<br \/>\n(c) 7 : 2<br \/>\n(d) 7: 3<br \/>\nAnswer:<br \/>\n(b) is correct<br \/>\n\\(\\frac{5 x+2 y}{3 x-y}=\\frac{5 \\times 2+2 \\times 3}{3 \\times 2-3}=\\frac{16}{3}\\)<\/p>\n<p>Question 33.<br \/>\nThe first, second and third month salaries of aperson are in the ratio 2:4:5. The difference between the product of the salaries of first 2 months &amp; last 2 months is \u20b9 4,80,00,000. Find the salary of the second month [1 Mark, Dec. 2014]<br \/>\n(a) \u20b9 4,000<br \/>\n(b) \u20b9 6,000<br \/>\n(c) \u20b9 12,000<br \/>\n(d) \u20b9 8,000<br \/>\nAnswer:<br \/>\n(d) is correct<br \/>\nLet x is common in the ratio.<br \/>\n1st, 2nd and 3rd month salaries of a person = 2x ; 4x ; 5x<br \/>\nFrom Qts.<br \/>\n4x \u00d7 5x &#8211; 2x \u00d7 4x = 4,80,00,000.<br \/>\nor, 12x<sup>2<\/sup> = 4,80,00,000.<br \/>\nor, x<sup>2<\/sup> = 4000000<br \/>\nx = 2000.<br \/>\n2nd month salary = 4x = 4&#215;2000<br \/>\n= \u20b9 8000<\/p>\n<p>Question 34.<br \/>\n(2p<sup>2<\/sup> &#8211; q<sup>2<\/sup>) = 7pq, where p, q are positive then p : q. [1 Mark, June 2015]<br \/>\n(a) 5:6<br \/>\n(b) 5:7<br \/>\n(c) 3:5<br \/>\n(d) 3:7<br \/>\nAnswer:<br \/>\n(a) is correct 15(2p<sup>2<\/sup> &#8211; q<sup>2<\/sup>) = 7pq<br \/>\nTricks : Go by choices<br \/>\nFor (a) put p = 5; q = 6 we get<br \/>\n15[2 \u00d7 5<sup>2<\/sup> &#8211; 6<sup>2<\/sup>] = 3 \u00d7 5 \u00d7 6<br \/>\nor 15 \u00d7 14 = 210<br \/>\nor 210 = 210<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p>Question 35.<br \/>\nIf one type of rice of cost \u20b9 13.84 is mixed with another type of rice of cost \u20b9 15.54, the mixture is sold at \u20b9 17.60 with a profit of 14.6% on selling price then in which proportion the two types of rice mixed ? [1 Mark, June 2015]<br \/>\n(a) 3:7<br \/>\n(b) 5:7<br \/>\n(c) 7:9<br \/>\n(d) 9:1<br \/>\nAnswer:<br \/>\nCost of mixture per kg = 17.60 &#8211; 14.6% = 15.0304 = 15.03 (approx.)<br \/>\nBy rules of Alligation<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-11583\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2023\/02\/Ratio-and-Proportion-\u2013-CA-Foundation-Maths-Study-Material-3.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material 3\" width=\"334\" height=\"286\" srcset=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2023\/02\/Ratio-and-Proportion-\u2013-CA-Foundation-Maths-Study-Material-3.png 334w, https:\/\/gstguntur.com\/wp-content\/uploads\/2023\/02\/Ratio-and-Proportion-\u2013-CA-Foundation-Maths-Study-Material-3-300x257.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\n51: 119 = 3: 7<br \/>\nGo by choices<br \/>\n(a) is correct (approx)<\/p>\n<p>Question 36.<br \/>\nFind the ratio of third proportional of 12 ; 30 and mean proportional of 9; 25 : [1 Mark, Dec. 2015]<br \/>\n(a) 7: 2<br \/>\n(b) 5 : 1<br \/>\n(c) 9 : 4<br \/>\n(d) None of these<br \/>\nAnswer:<br \/>\n3rd proportional = \\(\\frac{30^2}{12}\\) = 75<br \/>\nMean Proportional = \\(\\sqrt{9 \\times 25}\\) =15<br \/>\nRatio = \\(\\frac{75}{15}\\) = 5:1<br \/>\n(b) is correct<\/p>\n<p>Question 37.<br \/>\nWhat must be added to each of the numbers 10, 18, 22, 38 to make them proportional: [1 Mark, Dec. 2015]<br \/>\n(a) 5<br \/>\n(b) 2<br \/>\n(c) 3<br \/>\n(d) 9<br \/>\nAnswer:<br \/>\n(b) is correct<br \/>\nlet x be added.<br \/>\n\u2234 \\(\\frac{10+x}{18+x}=\\frac{22+x}{38+x}\\)<br \/>\nTricks: Go by choices.<br \/>\n\u2234 x = 2 satisfies it.<\/p>\n<p>Question 38.<br \/>\nx, y, z together starts a business, if x invests 3 times as much as y invests and y invests two third of what z invests, then the ratio of capitals of x, y, z is: [1 Mark, June 2016]<br \/>\n(a) 3 : 9 : 2<br \/>\n(b) 6: 3: 2<br \/>\n(c) 3 : 6 : 2<br \/>\n(d) 6: 2: 3<br \/>\nAnswer:(d)<br \/>\nTricks: Go by choices<br \/>\n6 = 3 \u00d7 2 and 2 = 3 \u00d7 \\(\\frac{2}{3}\\)<\/p>\n<p>Question 39.<br \/>\nA bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is ?\u20b9 43. The ratio between 1 rupee and 2 rupees coins is 3 : 2. Then the number of 1 rupee coins is: [1 Mark, Dec. 2016]<br \/>\n(a) 12<br \/>\n(b) 8<br \/>\n(c) 10<br \/>\n(d) 16<br \/>\nAnswer:<br \/>\n(a)<br \/>\nTricks : Go by choices<br \/>\nLet option (a) is correct.<br \/>\nLet x is common in the ratio.<br \/>\nSo, \u20b9 1 coins = 3x = 12 ; So, x = 4<br \/>\nNo. of \u20b9 2 coins = 2 \u00d7 4 = 8<br \/>\nHence no. of coins of \u20b9 5 coins = 23 &#8211; 12 &#8211; 8= 3<br \/>\nTotal money = 12 \u00d7 1 + 8 \u00d7 2 + 3 \u00d7 5 = \u20b9 43<br \/>\nSatisfied. So (a) is correct.<\/p>\n<p>Question 40.<br \/>\nIf a: b = 2: 3, b : c = 4: 5, c: d = 6: 7 then a : d is: [1 Mark, June 2017]<br \/>\n(a) 24 : 35<br \/>\n(b) 8 : 15<br \/>\n(c) 16 : 35<br \/>\n(d) 7 : 15<br \/>\nAnswer:<br \/>\nOption (c) is correct.<br \/>\nMultiply all ratios.<br \/>\n= \\(\\frac{2}{3} \\times \\frac{4}{5} \\times \\frac{6}{7}=\\frac{16}{35}\\)<\/p>\n<p>Question 41.<br \/>\nThe ratio of the number of five rupee coins to number of ten rupee coins is 8: 15. If the total value of five rupee coins is 360, then the no. of ten rupee coins is _______. [1 Mark, Dec. 2017]<br \/>\nAnswer:<br \/>\nOption (d) is correct.<br \/>\nTotal No. of \u20b9 5 coins = 360\/5 = 72<br \/>\nLet x is common in the ratio.<br \/>\nSo, \u20b9 5 coins = 8x = 72 ; So, x = 9<br \/>\nNo. of \u20b9 10 coins = 15 \u00d7 9 = 135<\/p>\n<p>Question 42.<br \/>\nIf \\(\\frac{1}{2}, \\frac{1}{3}, \\frac{1}{5}, \\frac{1}{x}\\) are in proportion then x = . [1 Mark, Dec. 2017]<br \/>\n(a) \\(\\frac{15}{2}\\)<br \/>\n(b) \\(\\frac{3}{15}\\)<br \/>\n(c) \\(\\frac{2}{15}\\)<br \/>\n(d) \\(\\frac{1}{15}\\)<br \/>\nAnswer:<br \/>\nOption (a) is correct.<br \/>\nProduct of middle two terms = Product of extremes<br \/>\nSo, \\(\\frac{1}{2 x}=\\frac{1}{15}\\); x = 15\/2<\/p>\n<p>Question 43.<br \/>\nIf (a + b): (b + c): (c + a) = 7 : 8 : 9 and a + b + c = 18 then a : b : c = . [1 Mark, June 2018]<br \/>\n(a) 5 : 4 : 3<br \/>\n(b) 3 : 4 : 5<br \/>\n(c) 4 : 3 : 5<br \/>\n(d) 4: 5 : 3<br \/>\nAnswer:<br \/>\n(c) 4 : 3 : 5 is correct<br \/>\nTricks: Go by choices.<br \/>\n(c) Let a : b : c = 4 : 3 : 5<br \/>\nIt is in ratio. So, it should must satisfy given ratio (a + b): (b + c): (c + a) = 7 : 8 : 9<br \/>\ni.e. (4 + 3): (3 + 5): (5 + 4) = 7 : 8 : 9 (True) Avoid 2nd condition.<br \/>\nIn detail it will take too much time.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gstguntur.com\/wp-content\/uploads\/2021\/10\/GST-Guntur.png\" alt=\"Ratio and Proportion \u2013 CA Foundation Maths Study Material\" width=\"123\" height=\"13\" \/><\/p>\n<p>Question 44.<br \/>\nIf p : q is the sub-duplicate ratio of p &#8211; x<sup>2<\/sup>:q &#8211; x<sup>2<\/sup>, then x<sup>2<\/sup> is : [1 Mark, May 2018]<br \/>\n(a) \\(\\frac{p}{p+q}\\)<br \/>\n(b) \\(\\frac{q}{p+q}\\)<br \/>\n(c) \\(\\frac{q p}{p-q}\\)<br \/>\n(d) None<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nThe mean proportional between 24 and 54 is : [1 Mark, May 2018]<br \/>\n(a) 33<br \/>\n(b) 34<br \/>\n(c) 35<br \/>\n(d) 36<br \/>\nSolution:<br \/>\nFormula<br \/>\nMean Proportion of a &amp; b = \\(\\sqrt{a b}\\)<br \/>\n(d) = \\(\\sqrt{24 \\times 54}\\) = 36<\/p>\n<p>Question 46.<br \/>\n\\(\\frac{3 x-2}{5 x+6}\\) is the duplicate ratio of \\(\\frac{2}{3}\\) then find the value of x : [1 Mark, Nov. 2018]<br \/>\n(a) 6<br \/>\n(b) 2<br \/>\n(c) 5<br \/>\n(d) 9<br \/>\nAnswer:<br \/>\n(a)<br \/>\nGiven \\(\\frac{3 x-2}{5 x+6}=\\left(\\frac{2}{3}\\right)^2=\\frac{4}{9}\\)<br \/>\nTricks : Go by choices<br \/>\nfor option (a) putting x = 6 in LHS; we get<br \/>\n\\(\\frac{3 \\times 2-2}{5 \\times 2+6}=\\frac{4}{9}\\)<br \/>\n\u2234 (a) is correct.<\/p>\n<p>Question 47.<br \/>\nIf x : y : z = 7 : 4 : 11 then is: [1 Mark, Nov. 2018]<br \/>\n(a) 2<br \/>\n(b) 3<br \/>\n(c) 4<br \/>\n(d) 5<br \/>\nAnswer:<br \/>\n(a)<br \/>\n\\(\\frac{x+y+z}{z}=\\frac{7+4+11}{11}\\) = 2<\/p>\n<p>Question 48.<br \/>\nIf the ratio of two numbers is 7 : 11. If 7 is added to each number then the new ratio will be 2 : 3 then the numbers are. [1 Mark, June 2019 ]<br \/>\n(a) 49,77<br \/>\n(b) 42,45<br \/>\n(c) 43,42<br \/>\n(d) 39,40<br \/>\nAnswer:<br \/>\nTricks:- GBC (Go by Choices)<br \/>\n(a)<br \/>\n49 \u00f7 7 = 7<br \/>\n77 \u00f7 11 = 7 both must be equal.<br \/>\nHere it is correct.<br \/>\nNow:<br \/>\n\\(\\frac{49+7}{77+7}=\\frac{56}{84}=\\frac{2}{3}\\)<br \/>\nDivide 56 by numerator (2) and 84 by Denominator (3) we get same value \u201c28\u201d<br \/>\nNote:- No need to solve ; only check.<br \/>\nBy Calculator.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This Ratio and Proportion \u2013 CA Foundation Maths Study Material\u00a0is designed strictly as per the latest syllabus and exam pattern. Ratio and Proportion \u2013 CA Foundation Maths Study Material Ratio: The comparison of two or more things of same kind is called Ratio. If x and y are two values of same kind (in same &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/gstguntur.com\/ratio-and-proportion-ca-foundation-maths-study-material\/\"> <span class=\"screen-reader-text\">Ratio and Proportion \u2013 CA Foundation Maths Study Material<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[160],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts\/11257"}],"collection":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/comments?post=11257"}],"version-history":[{"count":8,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts\/11257\/revisions"}],"predecessor-version":[{"id":11590,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts\/11257\/revisions\/11590"}],"wp:attachment":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/media?parent=11257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/categories?post=11257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/tags?post=11257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}