# Ratio and Proportion- Aptitude Questions and Answers

 In a bag, there are notes of 10, 20 and 50 in the ratio of 1 : 2 : 3. If the total money is 1000, how many notes of 10 are there? A) 5 B) 10 C) 15 D) 30 Correct Answer : 5 Explanation :Let the number of 10, 20 and 50 notes be X, 2X and 3X, respectively. Then , 10*X + 40*X + 150*X = 1000 X = 5 So, the number of 10 notes are, X = 5 If A = B*(2/3) and B = C *(4/5), then what will be A: B: C ? A) 12:8:10 B) 15:10:8 C) 10:15:12 D) 8:12:15 Correct Answer : 8:12:15 Explanation :A = B*(2/3) => A/B = 2/3 B = C *(4/5) => B/C = 4/5 So, A:B = 2:3 and B:C =4:5 Hence A:B:C =(2*4) :(3*4) :(3*5) =8:12:15 If the annual income of A, B and C is in the ratio of 1: 3: 7 and the total annual income of A and C is 800000, then what is the monthly salary of B? A) 20000 B) 25000 C) 30000 D) 15000 Correct Answer : 25000 Explanation :Let the monthly salary of A, B and C are X, 3X and 7X, then X+7x=800000 X=100000 Hence ,the monthly salary of B = 3*100000 / 12 => 25000 An examination of a school, the ratio of successful and unsuccessful candidates is 6: 1. If 6 more candidates are successful,then the ratio would be 9: 1 . What is the total number of candidates? A) 140 B) 120 C) 200 D) 160 Correct Answer : 140 Explanation :Let the successful candidates is 6X and unsuccessful candidates is X , then Therefore, 6X+6 / X - 6 = 9/1 6X+6 = 9X- 54 3X=60 X=20 Hence , Total candidates= 6X+ X =7X => 7*20 =>140 The ratio between the two numbers is 4: 5. If 4 is increased in each numbers , then the ratio becomes 3: 5. What is the greater number? A) 36 B) 48 C) 56 D) 64 Correct Answer : 56 Explanation :Let the numbers is 4X and 7X , then 4X+4 / 7X+ 4 = 3/5 20X+20 = 21X+12 X=8 Hence , greater number is= 7X=7*8 = 54 The ratio of two student numbers P and Q is 2: 5. If P's number is 120, then what is the Q's number? A) 120 B) 240 C) 300 D) 360 Correct Answer : 300 Explanation :Let the P's number is 2X and Q's number is 5X , then 2X = 120 Hence , Q's number = 5X=5*60 = 300 In a class of 49 students, the ratio of girls to boys is 4 : 3. If 4 girls leave the class, the ratio of girls to boys would be? A) 11 : 7 B) 8 : 7 C) 6 : 5 D) 9 : 8 Correct Answer : 8 : 7 Explanation :Let the number of girls be 4x and boys be 3x. 4x + 3x =49 7x=49 x=7 So,number of girls, 4x = 4*7 = 28 and number of boys, 3x = 3*7 = 21 Now 4 girls leave thus number of girls = 28 - 4 = 24 Hence, new ratio of girls to boys = 24/21 = 8/7 The respective ratio betwen the monthly salary of Om and that of Pihu is 7 : 9. Om and Pihu, both save 20% and 40% out of their respective monhtly salary. Om invest 1/2 of his savings in PPF and Pihu invests 7/9 of his savings in PPF. If Om and Pihu together saved 17500 in PPF, what is Pihu’s monthly salary? A) 72000 B) 36000 C) 45000 D) 40000 Correct Answer : 45000 Explanation :Let,Om and Pihu monthly salary be7x and 9x respectively. Now, saving of Om = 7x* 20/100 =7x/5 and saving of Pihu = 9x* 40/100 =18x/5 Om’s investement in PPF=7x/5 * 1/2 =7x/10 and Pihu’s investment in PPF=18x/5 * 7/9 =14x/5 Now, according to the question, 7x/10 + 14x/5 = 17500 7x/10 + 28x/10 = 17500 35x/10 = 17500 x = 175000/35 x = 5000 Pihu’s monthly salary = 9x = 9 * 5000 = 45000 By increasing the price of entry ticket to a fair in the ratio 3 : 7, the number of visitors to the fair has decreased in the ratio 16 : 13. In what ratio has the total collection increased or decreased? A) decreased in the ratio 91 : 48 B) increased in the ratio 48 : 91 C) increased in the ratio 39 : 112 D) decreased in the ratio 112 : 39 Correct Answer : increased in the ratio 48 : 91 Explanation :Total collection = Price of each entry ticket * number of visitors Increase in ratio = 16 * 3 : 13 * 7 = 48 : 91 If 2x=3y and 4y=5z, then what is x:z=? A) 3:4 B) 4:3 C) 15:8 D) 8:15 Correct Answer : 15:8 Explanation :2x = 3y => x=3y/2 4y = 5z => z= 4y/5 Hence, x:z = (3y/2) : (4y/5) = 15:8 What quantity must be added to each term of the ratio a + b : a – b to make it equal to (a + b)2 : (a – b)2 ? A) (a+b)/2a B) (b-1)/2a C) (b2 - a2 ) / 2a D) (a + b)/ (a – b) Correct Answer : (b2 - a2 ) / 2a Explanation :Let the X is quantity , then - (a + b) + x / (a – b) + x = (a + b)2/(a – b)2 ⇒ (a + b)(a – b)2 + (a – b)2.x = (a + b)2(a – b) + (a + b)2.x ⇒ (a + b)2.x - (a – b)2.x = (a + b)(a – b)2 - (a + b)2(a – b) ⇒ [a2 + b2 + 2ab - (a2 + b2 - 2ab )]x = (a + b)(a – b)(a – b) - (a + b)(a + b)(a – b) ⇒ [a2 + b2 + 2ab - (a2 + b2 - 2ab )]x = [ (a2 - b2)(a – b) – (a2 - b2) (a +b) ] ⇒ 4ab.x = (a2 - b2) [(a – b) – (a +b) ] ⇒ 4ab.x = -2b (a2 - b2) ⇒ x = (b2 - a2 ) / 2a In a school 4/9 of the pupils are boys. There are 125 girls. How many boys are there? A) 80 B) 100 C) 110 D) 120 Correct Answer : 100 Explanation :Let total people be x number of boys = 4x/9 So,number of girls = 1 - 4/9 = 5x/9 Then, 5x/9 = 125 x = 125* 9/5 = 25*9 x = 225 students So number of boys = 4x/9 = 4/9 *225 = 100 If A:B = 3:4 and B:C = 5:6, find A:C? A) 5:9 B) 3:4 C) 1:2 D) 5:8 Correct Answer : 5:8 Explanation :As is given B/C = 5/6 Then, B = (5/6)*C Substitute B value in A/B=3/4, Then, A/(5/6)*C = 3/4 A = (3/4)*(5/6)*C A/C = (3/4)*(5/6) A/C = 15/24 A/C = 5/8 So A : C = 5/8 IF X:Y = 3:4 AND Y:Z = 4:5, FIND X:Y:Z? A) 2 : 3 : 4 B) 3 : 4 : 5 C) 4 : 5 : 6 D) 5 : 6 : 7 Correct Answer : 3 : 4 : 5 Explanation :Given, X:Y = 3:4 X = 3Y / 4 Now, Y:Z = 4 : 5 5Y = 4Z Z = 5Y / 4 So, X : Y : Z = 3Y / 4 : Y : 5Y / 4 = 3Y / 4 : 4Y / 4 : 5Y / 4 = 3Y : 4Y : 5Y Therefore the ratio X:Y:Z = 3 : 4 : 5 Or X : Y = 3 : 4 = 3*4:4*4 = 12/16 Y : Z = 4 : 5 = 4*4:5*4 = 16/20 Therefore the ratio X:Y:Z = 12:16:20 = 3:4:5 If A:B = 2:3 and B:C = 9:5 find A:B:C? A) 2 : 3 : 4 B) 6: 9 : 5 C) 4 : 5 : 6 D) 5 : 6 : 7 Correct Answer : 6: 9 : 5 Explanation :Given, A:B = 2:3 A=2B/3 Now, B:C = 9:5 5B=9C C=5B/9 So, A:B:C = 2B/3 : B : 5B/9 = 9*2B/3 : 9*B : 9*5B/9 = 6: 9 : 5 Or A:B = 2:3 = 2*9:3*9 = 18/27 B:C = 9:5 = 9*3:5*3 = 27/15 Therefore the ratio A:B:C = 18 : 27 : 15 = 6:9:5 If A:B = 3/5:5/7 and B:C = 3/4:2/5, find A:B:C? A) 63:75:40 B) 65:75:80 C) 60:50:40 D) 60:70:80 Correct Answer : 63:75:40 Explanation :A:B = 3/5:5/7 = 3*7:5*5 = 21 : 25 B:C = 3/4:2/5 = 3*5:4*2 = 15 : 8 Therefore for the ratio A:B:C A:B = 21*15:25*15 B:C = 15*25:8*25 A:B:C =21*15 : 25*15 : 8*25 =21*3:25*3:8*5 =63:75:40