Question

Ranu's age is half of her mother's age now. Five years ago, the ratio of their ages was $4:9$. Ranu's current age is .

• A. 30
• B. 25
• C. 35
• D. 20

Answer 1

The correct option is B 25

Let the present age of Ranu's mother is $x$. The current age of Ranu is then $\frac{x}{2}.$

5 years ago the age of Ranu's mother was $(x-5)$ and Ranu was $(\frac{x}{2}-5)$ years old.

According to the given data,
$\frac{(\frac{x}{2}-5)}{(x-5)}=\frac{4}{9}$

Solving this equation, we get
$\Rightarrow 9(\frac{x}{2}-5)=4(x-5)\Rightarrow \frac{9x}{2}-45=4x-20\Rightarrow \frac{9x}{2}-4x=45-20\Rightarrow \frac{9x-8x}{2}=25\Rightarrow x=2\times 25\Rightarrow x=50$

Hence, Ranu's current age is $50÷2=25$ years