Ratio and Proportion- Aptitude Questions and Answers

 Priya broke her bangles as she slipped while walking. If she was wearing 12 bangles in her hands then which of the following cannot be the ratio of broken is to unbroken bangles? A) 1 : 1 B) 1 : 2 C) 1 : 3 D) 1 : 4 Correct Answer :1 : 4 Explanation :the sum of ratio must be a factor of 12 (1 x 12, 2 x 6, and 3 x 4) , that is 1, 2, 3, 4, 6 and 12 . So, they cannot be in the ratio 1 : 4 The ratio of incomes of A and B is 4:3 and their expenditures are in the ratio 3:2. If A saves one third of his income then find the ratio of their savings? A) 4:3 B) 9:7 C) 12:11 D) 4:5 Correct Answer :12:11 Explanation :Let, income of A and B are 4x and 3x,and their expenditure are 3y and 2y then there saving are 4x - 3y and 3x - 2y As given A save 1/3 rd of his income,then 4x - 3y = (1/3)*4x 12x - 9y = 4x x = 9y/8 then ratio of their saving = (4x - 3y)/(3x - 2y) = (36y/8 - 3y)/(27y/8 - 2y) = (36y-24y) / (27y-16y) = 12/11 The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 490, Krishan has ? A) Rs. 2890 B) Rs. 2330 C) Rs. 1190 D) Rs. 2680 Correct Answer :Rs. 2890 Explanation :a : b : c = A : B : C is equivalent to ,a/A = b/B = c/C Ram : Gopal = 7 : 17 = 49 : 119 Gopal : Krishan = 7 : 17 = 119 : 289 Then, Ram : Gopal : Krishan = 49 : 119 : 289 ⇒ Ram : Krishan = 49 : 289 Thus, 49 : 289 = 490 : X X= 289 * 490 / 49 = Rs. 2890 If 8 : y = y : 18 , then y is equal to ? A) 144 B) 72 C) 26 D) 12 Correct Answer :12 Explanation :a : b : c = A : B : C is equivalent to ,a/A = b/B = c/C 8 x 18 = y2 y = √144 = 12 The third proportional to 0.8 and 0.2 is ? A) 0.4 B) 0.8 C) 0.05 D) 0.032 Correct Answer :0.05 Explanation :Third Proportional: If a: b = b: c, then c is called the third proportional to a and b. Let 0.8 : 0.2 : : 0.2 : X Then 0.8 x X = 0.2 x 0.2 Thus, C = ( 0.2 x 0.2) / 0.8 = 0.04 / 0.08 = 4/80 = 0.05 The fourth proportional to 0.2, 0.12 and 0.3 is ? A) 0.13 B) 0.15 C) 0.18 D) 0.8 Correct Answer :0.18 Explanation :Fourth Proportional: If a : b = c: d, then d is called the fourth proportional to a, b, c. Let 0.2 : 0.12 : : 0.3 : X As, 0.2 * X = 0.12 * 0.3 Thus, X = (0.12 * 0.3) / 0.2 = 0.18 If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, then A : D is equal to ? A) 2 : 7 B) 7 : 8 C) 16 : 35 D) 4 : 13 Correct Answer :16 : 35 Explanation :(A/B) x (B/C) x (C/D) = (2/3) x (4/5) x (6/7) = 16/35 Thus, A : D = 16 : 35 A bag contains 25 paise, 10 paise and 5 paise coins in the ratio 1 : 2 : 3 . If their total value is 60, then the number of 5 paise coins is ? A) 10 B) 50 C) 30 D) 40 Correct Answer :30 Explanation :Let the number of 25 paise, 10 paise and 5 paise coins be X, 2X and 3X, respectively. Then , X + 2X + 3X = 60 ⇒ X = 10 Thus, The number of 5 paise coins = 3 x 10 = 30 Find the mean proportional between 9 and 64 ? A) 25 B) 24 C) 27 D) 35 Correct Answer :24 Explanation :Mean Proportional: Mean proportional between a and b is square root of ab. Mean proportional = √(9 x 64) = 3 x 8 = 24 Two numbers are in the ratio of 7:9, if we subtract 14 from each number the ratio will become 5:7. Find the sum of both the numbers? A) 112 B) 144 C) 128 D) 160 Correct Answer :112 Explanation :Let the numbers be 7x and 9x . When 14 is subtracted from both,then we get (7x-14):(9x-14) :: 5:7 49x - 98 = 45x - 70 4x = 28 x = 7 So the numbers are 49 and 63 ,and their sum =(49+63)= 112 The ratio of the number customers visited to a mall to those who purchased the clothes is 11:4. On a particular day 1320 customers visited to the mall. How many of these purchased the clothes? A) 320 B) 480 C) 360 D) 425 Correct Answer :480 Explanation :The ratio of number customers visited / customers who purchased the clothes =11 / 4 Let the X number of customers purchased the clothes So , 1320 / X =11 / 4 X=1320*4 /11 Thus number of customers purchased the clothes ,X = 480 The ratio of expenditure and savings of a person is 26: 3. If his monthly income is 7250, then what is his monthly savings? A) 290 B) 350 C) 750 D) 780 Correct Answer :750 Explanation :Let monthly expenditure = 26x and monthly savings = 3x Then, monthly income = 26x + 3x = 29x 29x = 7250 x = 250 Monthly savings = 3 * 250 = 750