# Problems on Ages Quiz Set 010

### Question 1

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.

### Question 2

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 3

P is 10 years older than Q, and Q's age is 4 times the age of R. If the sum of their ages today is 46, then what is the age of Q?

A

16 years.

B

17 years.

C

15 years.

D

18 years.

Soln.
Ans: a

Let the age of R be x. Then the age of Q is 4x, and that of P is 4x + 10. Adding the three ages, (4x + 10) + 4x + x = 46. Solving, we get x = 4. So the age of Q is 4x = 16 years.

### Question 4

The ratio of ages of P and Q today is \${1/2}\$. After 4 years, their ages will be in the ratio \${7/10}\$. What is the age of P today?

A

3 years.

B

4 years.

C

2 years.

D

5 years.

Soln.
Ans: a

Let the ages of P and Q be 1x and 2x. After 4 years the ratio would be \${1x + 4}/{2x + 4}\$ = \${7/10}\$. Solving, we get x = 3. So age of P = 1 × 3 = 3.

### Question 5

The sum of reciprocals of my ages 2 years back and 2 years later is \${70/1221}\$. What is my present age?

A

35 years.

B

36 years.

C

34 years.

D

37 years.

Soln.
Ans: a

Let the present age be x. Then \$1/{x + 2} + 1/{x - 2}\$ = \${70/1221}\$. 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}\$ = \${70/1221}\$. This can now be solved to give x = 35 years. 