Question

A person's present age is $\frac{2}{5}$th of the age of his mother. After $8$ years, he will be one-half of the age of his mother. How old is the mother at present?

• A. $32$ years
• B. $36$ years
• C. $40$ years
• D. $48$ years

Answer 1

Answer: (C)

$40$ years

Let the mother's present age $=x$ years
$\therefore$ Person's present age $=\frac{2}{5}x$ years
After $8$ years, it is given that

$\frac{2}{5}x+8=\frac{1}{2}(x+8)$

$\Rightarrow \frac{2}{5}x+8=\frac{1}{2}x+4$
$\Rightarrow \frac{1}{2}x-\frac{2}{5}x=4$
$\Rightarrow \frac{5}{10}x-\frac{4}{10}x=4$
$\Rightarrow x=40$

Threrefore, the age of mother is $40$ years.