Question

The ratio of present ages of Rehana and her mother $2:7$. After $2$ years, the ratio of their ages will be $1:3$. What is Rehana's present age?

Answer 1

Let present age of Rehana and her mother is

'x' & 'y' respectively

Given $\frac{x}{y}=\frac{2}{7}$ __ (1)

$\frac{x+2}{y+2}=\frac{1}{3}\Rightarrow 3x+6=y+2$

$\Rightarrow 3\times \frac{2y}{7}+6=y+2$

$\Rightarrow 4=y-\frac{6y}{7}$

$\Rightarrow 4=\frac{y}{7}=1y=28$

$\therefore x=8,y=28$

Hence, Rehana present age is '8' years old.