A father left a will of Rs. 16400 for his two sons aged 17 and 18 years. They must get equal amount when they are 20 years, at 5% compound interest. Find the present share of the younger son = ?

Answer: Option A

Let the share of the younger and elder sons be Rs. x and Rs. (16400 - x)
Then, amount of Rs. x after 3 years = Amount of Rs. (16400 - x) after 2 years
$$\begin{array}{rl}& \Rightarrow x{\left(1+\frac{5}{100}\right)}^3=\left(16400-x\right){\left(1+\frac{5}{100}\right)}^2\\ & \Rightarrow x\left(1+\frac{5}{100}\right)=\left(16400-x\right)\\ & \Rightarrow \frac{21x}{20}+x=16400\\ & \Rightarrow \frac{41x}{20}=16400\\ & \Rightarrow x=\left(\frac{16400\times 20}{41}\right)\\ & \Rightarrow x=8000\end{array}$$