Question

Bitu is 26 years younger than her mother. If after 16 years, the ratio of their ages is 15:28, then Bitu's present age is .

• A. 16
• B. 14
• C. 12
• D. 18

Answer 1

The correct option is B 14

Let the present age of Bitu be $x$
Her mother's age is $x+26$.
After 16 years their age will be $x+16$ and $x+26+16$ respectively.

According to question,
$\frac{x+16}{x+26+16}=\frac{15}{28}$
$\Rightarrow \frac{x+16}{x+42}=\frac{15}{28}$
$\Rightarrow 28(x+16)=15(x+42)$
$\Rightarrow 28x+448=15x+630$
$\Rightarrow 28x-15x=630-448$
$\Rightarrow 13x=182$
$\Rightarrow x=\frac{182}{13}$
$\Rightarrow x=14$

Hence, the present age of Bitu is 14 years.