Question : Rs. 16,820 is divided between two brothers of age 27 years and 25 years. They invested their money at 5% per annum compound interest in such a way that both will receive equal money at the age of 40 years. The share (in Rs.) of elder brother is:
Option 1: Rs. 8,280
Option 2: Rs. 8,410
Option 3: Rs. 8,820
Option 4: Rs. 8,000
Correct Answer: Rs. 8,820
Solution :
Suppose Share of elder brother = Rs. $y$
∴ Share of younger brother = Rs. $(16820 – y)$
Using the given formula,
$A=P(1+\frac{R}{100})^n$
According to the question,
$y(1+\frac{5}{100})^{13}=(16820-y)(1+\frac{5}{100})^{15}$
⇒ $y=(16820-y)(1+\frac{5}{100})^{2}$
⇒ $y=(16820-y)(\frac{21}{20})^{2}$
⇒ $y(\frac{20}{21})^{2}=(16820-y)$
⇒ $\frac{400y}{441}+y=16820$
⇒ $\frac{400y+441y}{441}=16820$
⇒ $\frac{881y}{441}=16820$
⇒ $y = 441×20 = 8820$
Hence, the answer is Rs. 8,820.
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