Question

A man’s age is now four times that of his son and it is also three times that of his daughter. In six years time it will be three times that of his son. How old was he when his daughter was born ?

(a) 48 years

(b) 26 years

(c) 32 years

(d) 40 years

Answer 1

Correct option is (c) 32 years

Let son's present age be x, and six years later his age will be (x + 6)

The present age of father will be 4x as his age is four times his son's age.

Six years later his age will be (4x + 6)

The present age of his daughter will be \(\frac{4x}3\)​ as the age of the father is three times of his daughter, so we can say that she is three times smaller than her father.

As per given question we can write the following equation,

⇒ 3(x + 6) = (4x + 6)

⇒ 3x + 18 = 4x + 6

⇒ 3x − 4x = 6 − 18

⇒ −x = −12

∴ x = 12

Since x = 12 present age of son is 12 yrs father is (4 × 12) = 48 and daughter is 

\(\left(\frac{4\times 12}3\right) = 16\)

Therefore age of father when his daughter was born was (48− 16) = 32