# Problems on Ages Quiz Set 020

### Question 1

The ratio of present ages of two monuments A and B is \$4{1/2}\$. After 7 years later the age of A will be 88 years. What is the present age of B?

A

18 years.

B

16 years.

C

14 years.

D

20 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${9/2}\$, which is same as: \$4{1/2}\$. So we can write the present ages of A and B, respectively, as 9r and 2r years. 7 years later the age of A is \$9r + 7 = 88\$ which gives r = 9. The age of B, therefore, is 2r = 2 × 9 = 18 years.

### Question 2

The sum of reciprocals of my ages 6 years back and 6 years later is \${13/160}\$. What is my present age?

A

26 years.

B

27 years.

C

25 years.

D

28 years.

Soln.
Ans: a

Let the present age be x. Then \$1/{x + 6} + 1/{x - 6}\$ = \${13/160}\$. 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 - 36}\$ = \${13/160}\$. This can now be solved to give x = 26 years.

### Question 3

The ratio of present ages of two monuments A and B is \$5{1/5}\$. If the difference of their ages is 105, then what is the age of B?

A

25 years.

B

20 years.

C

15 years.

D

30 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${26/5}\$, which is same as: \$5{1/5}\$. So we can write the present ages of A and B, respectively, as 26r and 5r years. The difference is \$26r - 5r = 105\$ which gives r = 5. The age of B, therefore, is 5r = 5 × 5 = 25 years.

### Question 4

Mr. X became a voter at the age of 18. He got married at the age of 32. What was his average age during these two points of his life?

A

25 years.

B

26 years.

C

24 years.

D

14 years.

Soln.
Ans: a

The average is simply \${18 + 32}/2\$ = 25 years.

### Question 5

The ages of three friends are in the ratio 17:2:13. What is the age of the youngest friend if the sum of their ages is 128 years?

A

8 years.

B

9 years.

C

7 years.

D

10 years.

Soln.
Ans: a

Let the ages of three friends be 17r, 2r and 13r. The youngest of these is 2r. We have been given their sum. So (17 + 2 + 13)r = 128. Solving, we get r = 4. The youngest is 2 × 4 = 8 years. 