Aptitude Questions: Ratio & Proportion Set 4

Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample in Ratio & Proportion , which is common for all the competitive  exams. We have included Some questions that are repeatedly asked in exams !!

1. A school has 4 sections of class 12, such that half the number of students of 1st section, 1/3rd of 2nd section, 1/4th of 3rd section and 1/5th of the 4th section are equal. If total number of students in class 12 is 420, find the number of students in sections 1st and 2nd.
   A) 180
   B) 120
   C) 240
   D) 150
   E) 260
   

   Answer & Explanation

   D) 150
   Explanation:
   Let number of students in 4 sections be A, B, C, D respectively. Then
   1/2 of A = 1/3 of b = 1/4 of C = 1/5 of D
   So A : B : C : D = 2 : 3 : 4 : 5            [When A/2 = B/3 = C/4, then ratio A: B : C = 2 : 3 : 4]
   So students in 1st and 2nd section = [(2+3)/(2+3+4+5)] * 420 = 150
   
   
   
2. The income of A, B, and C are in the ratio 3 : 4 : 7. If their incomes be changed such that the new income of A is 50% increased, 25% increased for B and 25% decrease for C. Find the ratio of their new incomes.
   A) 18 : 40 : 23
   B) 17 : 12 : 21
   C) 18 : 20 : 21
   D) 28 : 20 : 21
   E) None of these
   

   Answer & Explanation

   C) 18 : 20 : 21
   Explanation:
   Previous ratio = 3 : 4 : 7
   New ratio = (150/100) * 3 : (125/100) * 4 : (75/100) * 7
   
   
   
3. A, B and C divide Rs 4200 among themselves in the ratio 7 : 8 : 6. If Rs 200 is added to each of their shares, what is the new ratio in which they will receive the money?
   A) 9 : 8 : 7
   B) 8 : 9 : 7
   C) 8 : 9 : 8
   D) 9 : 10 : 8
   E) 7 : 9 : 8
   

   Answer & Explanation

   B) 8 : 9 : 7
   Explanation:
   A gets = [7/(7+8+6)] * 4200 = 1400
   B gets = [8/(7+8+6)] * 4200 = 1600
   C gets = [6/(7+8+6)] * 4200 = 1200
   Rs 200 added to each share, so new ratio =
   1400+200 : 1600+200 : 1200+200
   1600 : 1800 : 1400
   
   
   
4. The ratio of the monthly salaries of A and B is in the ratio 15 : 16 and that of B and C is in the ratio 17 : 18. Find the monthly income of C if the total of their monthly salary is Rs 1,87,450.
   A) Rs 66,240
   B) Rs 72,100
   C) Rs 62,200
   D) Rs 65,800
   E) Rs 60,300
   

   Answer & Explanation

   A) Rs 66,240
   Explanation:
   A/B = 15/16 and B/C = 17*18
   So A : B : C = 15*17 : 16*17 : 16*18
   = 255 : 272 : 288
   So C’s salary = [288/(255+272+288)] * 1,87,450
   
   
   
5. The ratio of the incomes of A and B last year was 9 : 13. Ratio of their incomes of last year to this year is 9 : 10 and 13 : 15 respectively. The sum of their present incomes is Rs 50,000. What is the present income of B?
   A) Rs 32,000
   B) Rs 24,000
   C) Rs 20,000
   D) Rs 30,000
   E) None of these
   

   Answer & Explanation

   D) Rs 30,000
   Explanation:
   Ratio of last year income to this year income of A is 9 : 10. So income of A last year is 9x and this year is 10x.
   Ratio of last year income to this year income of B is 13 : 15. So income of B last year is 13y and this year is 15y.
   So ratio of the incomes of A and B last year was 9x : 13y
   Now given that ratio of the incomes of A and B last year was 9 : 13.
   So 9x/13y = 9/13
   This gives x = y
   Total of incomes of A and B this year = 10x+15y = 10x+15x = 25 x              (because x=y)
   So 25x = 50,000
   This gives x = 2,000
   So present income of B = 15y = 15x = 15*2000 = 30,000
   
   
   
6. A sum of Rs 315 consists of 25 paise, 50 paise and 1 Re coins in the ratio 3 : 4 :6. What is the number of each kind of coin respectively?.
   A) 216, 144, 27
   B) 108, 144, 216
   C) 27, 72, 216
   D) 120, 35, 108
   E) 102, 150, 210
   

   Answer & Explanation

   B) 108, 144, 216
   Explanation:
   25 paise = 25/100 Rs, 50 paise = 50/100 Rs
   So value ratio of these coins become = 3*(25/100) : 4*(50/100) : 6*(1)
   = 3/4 : 2 : 6 = 3 : 8 : 24
   So 25 paise coins value= [3/(3+8+24)] * 315 = Rs 27, so coins = 27 * (100/25) = 108
   Similarly find others.
   
   
   
7. Rs 650 was divided among 3 children in the ratio 2 : 4 : 7. Had it been divided in the ratio 1/2 : 1/4 : 1/7, who would have gained the most and by how much?
   A) C, Rs 246
   B) C, Rs 264
   C) B, Rs 18
   D) A, Rs 246
   E) A, Rs 264
   

   Answer & Explanation

   E) A, Rs 264
   Explanation:
   New ratio = 1/2 : 1/4 : 1/7 = 14 : 7 : 4
   So both ratio suggests that C has not gained any money, rather he has lose the money.
   For both ratio find the shares of A and B
   With ratio 2 : 4 : 7, A gets = [2/(2+4+7)] * 650 = 100, B gets = [4/(2+4+7)] * 650 = 200
   With ratio 14 : 7 : 4, A gets = [14/(14+7+4)] * 650 = 364, B gets = [7/(14+7+4)] * 650 = 182
   B has also lose the money, A gain the money and = 364 – 100 = 264
   
   
   
8. The ratio of the number of boys to the number of girls in a school is 6 : 5. If 20% of boys and 45% of girls come by bus to school, what percentage of students opt transport other than bus to come to school?
   A) 68 9/11%
   B) 68 7/11%
   C) 72 7/11%
   D) 73%
   E) 73 5/11%
   

   Answer & Explanation

   B) 68 7/11%
   Explanation:
   If 20% of boys and 45% of girls come by bus, then 80% of boys and 55% of girls opt transport other than bus.
   Let total number of students in school = x
   So boys who opt other transport are (80/100) * 6/(6+5) * x = 24x/55
   And girls who opt other transport are (55/100) * 5/(6+5) * x = x/4
   So total students who opt other transport = (24x/55) + (x/4) = 151x/220
   So required % = [(151x/220)/x] * 100 = 755/11 %
   
   
9. The incomes of A and B are in the ratio 1 : 2 and their expenditures are in the ratio 2 : 5. If A saves Rs 20,000 and B saves Rs 35,000, what is the total income of A and B?
   A) Rs 30,000
   B) Rs 90,000
   C) Rs 90,000
   D) Rs 60,000
   E) Rs 80,000
   

   Answer & Explanation

   C) Rs 90,000
   Explanation:
   Income of A = x, of B = 2x
   Expenditure of A = 2y, of B = 5y
   Savings is (income – expenditure). So
   x – 2y = 20,000
   2x – 5y = 35,000
   Solve the equations, x = 30,000
   So total = x+2x = 3x = 3*30,000 = 90,000
   
   
   
10. Rs 5750 is divided among A, B, and C such that if their share be reduced by Rs 10, Rs 15 and Rs 25 respectively, the reminder amounts with them shall be in the ratio 4 : 6 : 9. What was C’s share then?
    A) Rs 2700
    B) Rs 2725
    C) Rs 2750
    D) Rs 2625
    E) None of these
    

    Answer & Explanation

    B) Rs 2725
    Explanation:
    When the shares reduce, the total amount will also reduce which is to be divided among them. So after reducing shares by Rs 10, Rs 15 and Rs 25 respectively, total amount is 5750 – (10+15+25) = 5700
    So C’s share shall be [9/(4+6+9)] * 5700 = 2700
    Actually C would have received = 2700 + 25