Question

Arun is now half as old as his father. Twelve years ago the fathers age was three times as old as Arun. Find their present ages

Answer 1

Let Aruns age be $x$ years now.
Then his fathers age $=2x$ years
$12$ years ago, Aruns age was $(x-12)$ years and his fathers age was $(2x-12)$ years.
Given that, $(2x-12)=3(x-12)$
$2x-12=3x-36$
$36-12=3x-2x$
$x=24$
Therefore, Arun's present age $=24years$.
His father's present age $2\left(24\right)=48years$.

Verification:

Arun's age	Father'a age
Now : $24$	$48$
$12$ years ago $24-12=12$	$48-12=36$ $36=3$ (Arun's age) $=3\left(12\right)=36$