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 = ?

1Rs. 8000
2Rs. 8200
3Rs. 8400
4Rs. 8800

Answer:- 1

Explanation:-

Solution:

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{aligned} \Rightarrow x {(1 + \frac{5}{100})}^{3} = (16400 - x) {(1 + \frac{5}{100})}^{2} \\ \Rightarrow x (1 + \frac{5}{100}) = (16400 - x) \\ \Rightarrow \frac{21 x}{20} + x = 16400 \\ \Rightarrow \frac{41 x}{20} = 16400 \\ \Rightarrow x = (\frac{16400 \times 20}{41}) \\ \Rightarrow x = 8000 \end{aligned}

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