Question

The present age of a father is three times that of his elder son. Four years hence, the age of the father will be four times that of his younger son. If the difference between the present ages of the elder and younger child is 6 years, what is the present age of the father?
1. 36 years
2. 38 years
3. 42 years
4. 32 years

Answer 1

Correct Answer - Option 1 : 36 years

(1) The present age of a father is three times that of his elder son.

Let the present age of father be F and that of elder son's be E, then:

F = 3 × E

(2) Four years hence, the age of the father will be four times that of his younger son.

Let the present age of younger son be Y, then:

F + 4 = 4 × (Y + 4)

(3) If the difference between the present ages of the elder and younger child is 6 years, then:

E - Y = 6 ⇒ E = Y + 6, 

From above three statements,

⇒ F = 3Y + 18 (from (1) and (3))

⇒ Y = (F - 18) ÷ 3

Now, substituting Y in (2)

⇒ \(F + 4 = 4 × [{(F - 18) \over 3} + 4]\)

⇒ \({F\over 4} + 1= {F \over 3} - 6 + 4\)

⇒ \({F \over 3} - {F\over 4} = 3\)

⇒ F = 3 × 12

⇒ F = 36

Hence, the present age of father is 36 years.