Question

The age of Sulekha and Arunima are in the ratio $9:8$ respectively. After $5$ years, the ratio of their ages will be $10:9$. What is the difference between their ages?

• A. $4$ years
• B. $5$ years
• C. $6$ years
• D. $7$ years

Answer 1

The correct option is B $5$ years

Let the present ages of Sulekha and Arunima be $x$ and $y$ respectively.
The age of Sulekha and Arunima are in the ratio $9:8$ respectively.
$\therefore$ $\frac{x}{y}=\frac{9}{8}$
$\therefore$ $8x-9y=0$ ...(1)
After $5$ years, the ratio of their ages will be $10:9$.
$\therefore$ $\frac{x+5}{y+5}=\frac{10}{9}$
$\therefore$ $9x-10y=5$ ...(2)
Subtracting (2) and (1), we get
$x-y=5$
$\therefore$ Difference between their ages is $x-y=5$.