The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?

Answer: Option A

Let Shakti's age be 8$$x$$ years,
Then Kanti's age = 7$$x$$ years
$$\begin{array}{rl}& \therefore \frac{8x+10}{7x+10}=\frac{13}{12}\\ & \Rightarrow 12\left(8x+10\right)=13\left(7x+10\right)\\ & \Rightarrow 96x+120=91x+130\\ & \Rightarrow 5x=10\\ & \Rightarrow x=2\end{array}$$
Difference between their ages
$$\begin{array}{rl}& =\left(8x-7x\right)\\ & =x\text{years}\\ & \text{ = 2}\text{years}\end{array}$$