# Problems on Ages Quiz Set 017

### Question 1

The ages of two friends are 4 and 9 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

6 years.

B

7 years.

C

5 years.

D

8 years.

Soln.
Ans: a

If the age of the third friend is x. Then for a GP, x = \$√(4 × 9)\$ = 6 years.

### Question 2

The sum of reciprocals of my ages 2 years back and 2 years later is \${74/1365}\$. What is my present age?

A

37 years.

B

38 years.

C

36 years.

D

39 years.

Soln.
Ans: a

Let the present age be x. Then \$1/{x + 2} + 1/{x - 2}\$ = \${74/1365}\$. 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 \${2x}/{x^2 - 4}\$ = \${74/1365}\$. This can now be solved to give x = 37 years.

### Question 3

P is 10 years older than Q, and Q's age is 7 times the age of R. If the sum of their ages today is 85, 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 + 10. Adding the three ages, (7x + 10) + 7x + x = 85. Solving, we get x = 5. So the age of Q is 7x = 35 years.

### Question 4

The ages of two friends are in the ratio 23:11. What is the age of the younger friend if the sum of their ages is 68 years?

A

22 years.

B

23 years.

C

21 years.

D

24 years.

Soln.
Ans: a

Let the ages be 23r and 11r. The younger is 11r. We have been given their sum. So (23 + 11)r = 68. Solving, we get r = 2. The younger is 11 × 2 = 22 years.

### Question 5

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 14 years back, if the age of the mother today is 50 years?

A

11 years.

B

12 years.

C

10 years.

D

13 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 50/2 = 25 years. And, 14 years back the age of the daughter was 25 - 14 = 11 years.