Question

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

Answer 1

Let the present age of Rehana be $x$

Ratio of present ages of Rehana & her mother $=\frac{2}{7}$

$\frac{x}{Prsentageofmother}=\frac{2}{7}$

Present age of mother $=\frac{7x}{2}$

After $2$ years :-

Rehana's age $=x+2$

Rehana's mother's age $=\frac{7x}{2}+2$

Now,

Ratio $=\frac{x+2}{\frac{7x}{2}+2}=\frac{1}{3}$

cross multiplying

$3x+6=\frac{7x}{2}+2$

$\frac{7x}{2}-3x=4$

$\frac{7x-6x}{2}=4\Rightarrow x=8$

$\therefore$ Rehana's present age $=8$ years