Ratio & Proportion Aptitude Questions

Q1. 1: 3 = 1 2/3: x. The value of x is?

x * 1 = 3 * 5/3

x = 5

Q2. Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's present salary?

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

Then, (2x + 4000)/(3x + 4000) = 40/57

6x = 68000 => 3x = 34000

Sumit's present salary = (3x + 4000) = 34000 + 4000 = Rs. 38,000.

Q3. If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively:

(A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4

A:B = 2:3 and B:C = 1:4 = 3:12

A:B:C = 2:3:12

A;s share = 510 * 2/17 = Rs. 60

B's share = 510 * 3/17 = Rs. 90

C's share = 510 * 12/17 = Rs. 360.

Q4. The sum of three numbers is 98. If the ratio of the first to the second is 2:3. And that of the second to the third is 5:8, then the second number is:

Let the three parts A, B, C.

Then, A:B = 2:3 and B:C = 5:8

= (5 * 3/5) : (8 * 3/5) = 3:24/5

A:B:C = 2:3:24/5

= 10:15:24 => B = 98 * 15/49 = 30.

Q5. A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?

4/15 A = 2/5 B => A = (2/5 * 15/4)B

A =3/2 B => A/B = 3/2 => A:B = 3:2

B's share = 1210 * 2/5 = Rs. 484.

Q6. Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased sears are (140% of 5x), (150% of 7x) and (175% of 8x)

i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)

i.e., 7x, 21x/2 and 14x

Required ratio = 7x:21x/2:14x

= 14x : 21x : 28x = 2:3:4

Q7. The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

i.e., (120/100 * 7x) and (110/100 * 8x)

i.e., 42x/5 and 44x/5

Required ratio = 42x/5 : 44x/5 = 21:22

Q8. A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?

Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.

Then, 4x - 3x = 1000 => x = 1000.

B's share = Rs. 2x = 2 * 1000 = Rs. 2000.

Q9. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

Let 40% of A = 2/3 B. Then,

40A/100 = 2B/3 => 2A/5 = 2B/3

A/B = (2/3 * 5/2) = 5/3

A:B = 5:3.

Q10. Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?

Let the original earnings of A and B be Rs. 4x and Rs. 7x.

New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x

New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4

6x:21x/4 = 8:7

This does not give x. So, the given data is inadequate.