Question

A father is twice as old as his son. $20$ years back, he was twelve times as old as his son. What are their present ages ?

• A. $24$ years, $12$ years
• B. $44$ years, $22$ years
• C. $48$ years, $44$ years
• D. None of these

Answer 1

The correct option is B $44$ years, $22$ years

Let the age of son be $x$ years and father be $2x$ years.
$20$ years back, their ages were $x-20$ and $2x-20$
As per the given condition, we get

$2x-20=12(x-20)$

$\Rightarrow 2x-20=12x-240$
$\Rightarrow 2x-12x=20-240$
$\Rightarrow -10x=-220$
$\Rightarrow x=\frac{220}{10}$

$\Rightarrow x=22$

$\therefore$ son's age is $22$ years and father's age is $(2\times 22)=44$ years.