# Problems on Ages Quiz Set 014

### Question 1

Each year the ages of three friends are in an AP(arithmetic progression). The age of middle friend today is 37 years. What would be the sum of their ages 10 years from now?

A

141 years.

B

142 years.

C

140 years.

D

143 years.

Soln.
Ans: a

Let the present ages of the three friends be a - d, a and a + d. As of today a = 37. Ten years later their ages would be a + 10 - d, a + 10, a + 10 + d. Adding these we get 3a + 30 which equals 3 × 37 + 30 = 141 years.

### Question 2

The sum of the ages of 4 calves of a whale born at a gap of 2 years is 52. What is the age of the youngest calf?

A

10 years.

B

11 years.

C

9 years.

D

12 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 2, n = 4, and sum S = 52. We have to find the first term a. We know S = \${n/2} × (2a + (n-1)d)\$ Putting the values 52 = \${4/2} × (2a + (4-1)×2)\$. Solving, get a = 10 years.

### Question 3

When the daughter was born, the age of her mother was same as the daughter's age today. What was the age of the daughter 16 years back, if the age of the mother today is 58 years?

A

13 years.

B

14 years.

C

12 years.

D

15 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 58/2 = 29 years. And, 16 years back the age of the daughter was 29 - 16 = 13 years.

### Question 4

The ages of three friends are in the ratio 3:19:7. What is the age of the youngest friend if the sum of their ages is 174 years?

A

18 years.

B

19 years.

C

17 years.

D

20 years.

Soln.
Ans: a

Let the ages of three friends be 3r, 19r and 7r. The youngest of these is 3r. We have been given their sum. So (3 + 19 + 7)r = 174. Solving, we get r = 6. The youngest is 3 × 6 = 18 years.

### Question 5

The square root of twice my present age is equal to the sum of the square roots of my ages 8 years back and 8 years hence. What is my present age?

A

8 years.

B

9 years.

C

7 years.

D

16 years.

Soln.
Ans: a

Let the present age be x. Then \$√(x - 8) + √(x + 8)\$ = \$√{2x}\$. Squaring both sides, \$(√(x - 8))^2 + (√(x + 8))^2 + 2√{x^2 - 8^2}\$ = \$2x\$ which gives \$x - 8 + x + 8 + 2√{x^2 - 8^2}\$ = \$2x\$. Cancelling, and simplifying, \$2√(x^2 - 64) = 0\$, which leads to x = 8 years.