# Problems on Ages Quiz Set 002

### Question 1

The ages of two friends are in the ratio 3:5. What is the age of the younger friend if the sum of their ages is 24 years?

A

9 years.

B

10 years.

C

8 years.

D

11 years.

Soln.
Ans: a

Let the ages be 3r and 5r. The younger is 3r. We have been given their sum. So (3 + 5)r = 24. Solving, we get r = 3. The younger is 3 × 3 = 9 years.

### Question 2

The ages of three friends are in the ratio 19:2:3. What is the age of the youngest friend if the sum of their ages 5 years back was 129 years?

A

12 years.

B

13 years.

C

11 years.

D

14 years.

Soln.
Ans: a

Let the ages of three friends be 19r, 2r and 3r. The youngest of these is 2r. We have been given their sum 5 years back. So (19 + 2 + 3)r - (3 × 5) = 129. Solving, we get r = 6. The youngest is 2 × 6 = 12 years.

### Question 3

The sum of the ages of 12 calves of a whale born at a gap of 8 years is 672. What is the age of the youngest calf?

A

12 years.

B

13 years.

C

11 years.

D

14 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 8, n = 12, and sum S = 672. We have to find the first term a. We know S = \${n/2} × (2a + (n-1)d)\$ Putting the values 672 = \${12/2} × (2a + (12-1)×8)\$. Solving, get a = 12 years.

### Question 4

The sum of the ages of 14 calves of a whale born at a gap of 8 years is 924. What is the age of the youngest calf?

A

14 years.

B

15 years.

C

13 years.

D

16 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 8, n = 14, and sum S = 924. We have to find the first term a. We know S = \${n/2} × (2a + (n-1)d)\$ Putting the values 924 = \${14/2} × (2a + (14-1)×8)\$. Solving, get a = 14 years.

### Question 5

The sum of ages of two friends is 15, whereas the product of their ages is 54. What is the sum of squares of their ages?

A

117 years.

B

118 years.

C

116 years.

D

119 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 15, and xy = 54. Substituting in the identity \$x^2 + y^2 = (x + y)^2 - 2 × xy\$, we get \$x^2 + y^2 = 15^2 - 2 × 54\$ = 117.