# Problems on Ages Quiz Set 020

### Question 1

The ages of three friends are in the ratio 2:3:17. What is the age of the youngest friend if the sum of their ages 3 years back was 35 years?

A

4 years.

B

5 years.

C

3 years.

D

6 years.

Soln.
Ans: a

Let the ages of three friends be 2r, 3r and 17r. The youngest of these is 2r. We have been given their sum 3 years back. So (2 + 3 + 17)r - (3 × 3) = 35. Solving, we get r = 2. The youngest is 2 × 2 = 4 years.

### Question 2

P is 13 years older than Q, and Q's age is 7 times the age of R. If the sum of their ages today is 88, then what is the age of Q?

A

35 years.

B

36 years.

C

34 years.

D

37 years.

Soln.
Ans: a

Let the age of R be x. Then the age of Q is 7x, and that of P is 7x + 13. Adding the three ages, (7x + 13) + 7x + x = 88. Solving, we get x = 5. So the age of Q is 7x = 35 years.

### Question 3

The ratio of ages of P and Q today is \${14/47}\$. After 6 years, their ages will be in the ratio \${5/16}\$. What is the age of P today?

A

84 years.

B

85 years.

C

83 years.

D

86 years.

Soln.
Ans: a

Let the ages of P and Q be 14x and 47x. After 6 years the ratio would be \${14x + 6}/{47x + 6}\$ = \${5/16}\$. Solving, we get x = 6. So age of P = 14 × 6 = 84.

### Question 4

The ages of two friends are 9 and 16 years respectively. They are looking for a special third friend whose age is in-between their ages. What should be the age of the third friend if the ages of all three have to be in a GP(geometric progression)?

A

12 years.

B

13 years.

C

11 years.

D

14 years.

Soln.
Ans: a

If the age of the third friend is x. Then for a GP, x = \$√(9 × 16)\$ = 12 years.

### Question 5

P is 13 years older than Q, and Q's age is 6 times the age of R. If the sum of their ages today is 117, then what is the age of Q?

A

48 years.

B

49 years.

C

47 years.

D

50 years.

Soln.
Ans: a

Let the age of R be x. Then the age of Q is 6x, and that of P is 6x + 13. Adding the three ages, (6x + 13) + 6x + x = 117. Solving, we get x = 8. So the age of Q is 6x = 48 years.