The ages 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 in their ages ?

Answer: Option B

Let Sulekha age be 9 year,
Then Arunima's age = 8x years
$$\begin{array}{rl}& \frac{9x+5}{8x+5}=\frac{10}{9}\\ & \Rightarrow 9\left(9x+5\right)=10\left(8x+5\right)\\ & \Rightarrow 81x+45=80x+50\\ & \Rightarrow x=5\end{array}$$
Difference in their ages
= (9x - 8x) years
= x years
= 5 years