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 = ?

Solution(By Examveda Team)

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
$$\eqalign{ & \Rightarrow x{\left( {1 + \frac{5}{{100}}} \right)^3} = \left( {16400 - x} \right){\left( {1 + \frac{5}{{100}}} \right)^2} \cr & \Rightarrow x\left( {1 + \frac{5}{{100}}} \right) = \left( {16400 - x} \right) \cr & \Rightarrow \frac{{21x}}{{20}} + x = 16400 \cr & \Rightarrow \frac{{41x}}{{20}} = 16400 \cr & \Rightarrow x = \left( {\frac{{16400 \times 20}}{{41}}} \right) \cr & \Rightarrow x = 8000 \cr} $$