Question

Vandhana is four times as old as her brother Akash at present.After $10$ years, she will be twice the age of her brother.Find their present ages.

Answer 1

Let the present age of Akash be $=x$ years

$\therefore$ present age of Vandhana$=4x$ years

After $10$ years, the age of Akash will be $=x+10$ years

the age of Vandhana will be $=4x+10$ years.

According to the problem,

$4x+10=2(x+10)$

$\Rightarrow 4x+10=2x+20$

$\Rightarrow 4x-2x=20-10$

$\Rightarrow 2x=10$

$\Rightarrow x=\frac{10}{2}=5$

$\therefore$ present age of Akash is $5$ years and present age of Vandhana is $4x=4\times 5=20$ years.