A father left a will of ₹ 16400 for his two sons aged 17 and 18 years. They must get equal amounts when they are 20 years, at 5\% compound interest. Find the present share of the younger son. (R.R.B., 2008)
(a)` 8000
(b)` 8200
(c)` 8400
(d)` 8800
Answer
Answer (as printed): A
Explanation
Let the shares of the younger and elder sons be ₹ $x$ and ₹ $(16400-x)$. Then, Amount of ₹ $x$ after 3 years = Amount of ₹ (16400 $-x)$ after 2 years $$\begin{aligned} & \Rightarrow x\left(1+\frac{5}{100}\right)^{3}=(16400-x)\left(1+\frac{5}{100}\right)^{2} \\ & \Rightarrow x\left(1+\frac{5}{100}\right)=(16400-x) \\ & \Rightarrow \frac{21 x}{20}+x=16400 \\ & \Rightarrow \frac{41 x}{20}=16400 \\ & \Rightarrow x=\left(\frac{16400 \times 20}{41}\right)=8000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.