# Problems on Ages Quiz Set 008

### Question 1

My father was 25 years old when I was born. My mother's age was 18 when my sister, who is 6 years younger to me, was born. What is the difference between the ages of my parents?

A

13 years.

B

14 years.

C

12 years.

D

15 years.

Soln.
Ans: a

If the age of my father is F, then my age is F - 25, so my younger sister's age is (F - 25) - 6, which is = F - 31. If my mother's age is M, then M = (my sister's age) + 18, i.e., M = (F - 31) + 18. We get F - M = 13 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 25 + 6 = 31. At the time my mother was 18 years. So the difference between their ages = 31 - 18 = 13 years.

### Question 2

The ratio of ages of P and Q today is \${29/59}\$. After 3 years, their ages will be in the ratio \${119/239}\$. What is the age of P today?

A

116 years.

B

117 years.

C

115 years.

D

118 years.

Soln.
Ans: a

Let the ages of P and Q be 29x and 59x. After 3 years the ratio would be \${29x + 3}/{59x + 3}\$ = \${119/239}\$. Solving, we get x = 4. So age of P = 29 × 4 = 116.

### Question 3

The sum of the ages of 10 calves of a whale born at a gap of 4 years is 280. 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 = 4, n = 10, and sum S = 280. We have to find the first term a. We know S = \${n/2} × (2a + (n-1)d)\$ Putting the values 280 = \${10/2} × (2a + (10-1)×4)\$. Solving, get a = 10 years.

### Question 4

My present age is 432 times the reciprocal of my age 6 years back. What is my present age?

A

24 years.

B

25 years.

C

23 years.

D

26 years.

Soln.
Ans: a

Let the present age be x. Then \$x = 432/{x - 6}\$. At this stage a better option is that you try putting the given answers into this expression one by one. The other option is to simplify this expression into a quadratic equation \$x × (x - 6)\$ = 432. This can now be solved to give x = 24 years.

### Question 5

Mr. X became a voter at the age of 18. He got married at the age of 24. What was his average age during these two points of his life?

A

21 years.

B

22 years.

C

20 years.

D

6 years.

Soln.
Ans: a

The average is simply \${18 + 24}/2\$ = 21 years.