# Problems on Ages Quiz Set 014

### Question 1

The sum of ages of two friends is 20, whereas the product of their ages is 91. What is the sum of squares of their ages?

A

218 years.

B

219 years.

C

217 years.

D

220 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 20, and xy = 91. Substituting in the identity \$x^2 + y^2 = (x + y)^2 - 2 × xy\$, we get \$x^2 + y^2 = 20^2 - 2 × 91\$ = 218.

### Question 2

The sum of reciprocals of my ages 6 years back and 6 years later is \${16/247}\$. What is my present age?

A

32 years.

B

33 years.

C

31 years.

D

34 years.

Soln.
Ans: a

Let the present age be x. Then \$1/{x + 6} + 1/{x - 6}\$ = \${16/247}\$. 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}\$ = \${16/247}\$. This can now be solved to give x = 32 years.

### Question 3

The ages of two friends are 4 and 25 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

10 years.

B

11 years.

C

9 years.

D

12 years.

Soln.
Ans: a

If the age of the third friend is x. Then for a GP, x = \$√(4 × 25)\$ = 10 years.

### Question 4

The ratio of present ages of two monuments A and B is \$1{9/11}\$. If the difference of their ages is 117, then what is the age of B?

A

143 years.

B

132 years.

C

121 years.

D

154 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${20/11}\$, which is same as: \$1{9/11}\$. So we can write the present ages of A and B, respectively, as 20r and 11r years. The difference is \$20r - 11r = 117\$ which gives r = 13. The age of B, therefore, is 11r = 11 × 13 = 143 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 5 years back, if the age of the mother today is 44 years?

A

17 years.

B

18 years.

C

16 years.

D

19 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 44/2 = 22 years. And, 5 years back the age of the daughter was 22 - 5 = 17 years.