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Q.

The father's age is six times his son's age. Four years hence, the age of the father will be four times his son. The present ages (in years) of the son and the father are, respectively

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a

4 and 24

b

5 and 30

c

6 and 36

d

7 and 35

answer is C.

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Detailed Solution

Given that the father's age is six times his son's age. Four years hence, the age of the father will be four times his son.
We know that a pair of linear equations with two variables x and y has the following generic form,

a 1 x + b 1 y + c 1 = 0

and,

a 2 x + b 2 y + c 2 = 0

, where

a 1, a 2, b 1, b 2, c 1, c 2

are constants.
Let us assume that the present age of father as x years and the present age of son as y years.
Given that the father age is six times his son's age means it can be represented as,

x = 6 y .

The age of the father after four years is

(x + 4)

years
The age of son after four years is

(y + 4)

Years.
Also given after four years, the age of the father will be four times his son's age means it can be represented as,

(x + 4) = 4 (y + 4)

Substitute x=6y in

(x + 4) = 4 (y + 4)

to obtain the value of y. So,

(x + 4) = 4 (y + 4) 6 y + 4 = 4 y + 16 6 y − 4 y = 16 − 4 2 y = 12

y = 122 = 6 years

Substitute the value of y in

x = 6 y

to obtain the value of x.
Therefore,

x = 6 × 6 ⇒ x = 36 years

So, the present age of son and father are 6 years and 36 years respectively.
Therefore, option (3) is correct.

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