Question

A father divides his property between his two sons A and B. A invests the amount at compound interest of $8\%$ p.a. B invests the amount at 10% p.a simple interest. At the end of $2$ years , the interest received by B is Rs $1336$ more than the interest received by A. Find A 's share in the father's father's property of Rs $25,000$.

• A. Rs $12,000$
• B. Rs $13,000$
• C. Rs $10,000$
• D. Rs $12,500$

Answer 1

Answer: (C)

Rs $10,000$

$\Rightarrow$ Suppose A gets $Rs.P$ and B gets $Rs.(25000-P)$.

$\Rightarrow$ Interest received by A at the rate 8% per annum C.I.

$\Rightarrow$ $P(1+\frac{8}{100}{)}^2-P$

$\Rightarrow$ $P(\frac{27}{25}{)}^2-P$

$\Rightarrow$ $\frac{104P}{625}$

$\Rightarrow$ Interest received by B at the rate of 10% per annum S.I.

$\Rightarrow$ $\frac{\left[\right(25000-P)\times 10\times 2]}{100}=\frac{25000-P}{5}$

$\Rightarrow$ According to the question,

$\Rightarrow$ $\frac{(25000-P)}{5}=\frac{104P}{625}+1336$

$\therefore$ $P=Rs.10,000$