Question

The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio 7 : 4. Find their present ages.

Answer 1

Let present age of son = x year

Then age of his father = 2x

8 years hence,

Age of son = (x+8) years

and age of father = (2x + 8) years

According to the condition,

$\frac{2x+8}{x+8}=\frac{7}{4}$

$\Rightarrow$ 8x + 32 = 7x + 56

$\Rightarrow$ 8x - 7x = 56 - 32 $\Rightarrow$ x = 24

$\therefore$ Present age of son = 24 years

and age of father = 2x = 2 $\times$ 24 = 48 years

Hence age of man = 48 years and age of his son = 24 years