Question

The sum of the ages of father and son at present is 48 years. Six years ago the product of their age was equal to five times the present age of the father. Find the age of the father when the son was born.  
1. 26 yrs
2. 25 yrs
3. 24 yrs
4. 27 yrs
5. 28 yrs

Answer 1

Correct Answer - Option 3 : 24 yrs

GIVEN:

(Father + son)'s age = 48 yrs

(Father × son)'s age six years ago = 5 × father's age

EXPLANATION:

Let the age of father be x yrs.

son's age = 48 - x

Ages 6 years ago = x - 6, 42 - x

A.T.Q

(x – 6) (42 – x) = 5 × x

42x – x² – 252 + 6x = 5x

x² – 43x + 252 = 0

x² – 36x – 7x + 252 = 0

(x – 7) (x – 36) = 0

x = 36, 7

Father's age can't be 7 so,

x = 36 yrs

Son's age = 48 – 36 = 12 years

Requires age = 36 – 12 = 24 yrs

∴ The father was 24 years old.