Question

Divide Rs. 36,465 between A and B so that when their shares are lent out at 10 per cent compound interest per year, the amount that A receives in 7 years is the same as what B receives in 5 years.

Answer 1

Let A's share = Rs. x
B's share = Rs (36465 - x)
Given : Amount of A in 7 years = Amount of B in 5 years
$\Rightarrow {x(1+\frac{10}{100})}^7=(36465-x){(1+\frac{10}{100})}^5$
$\Rightarrow {x(1+\frac{10}{100})}^2=36465-x$

$\Rightarrow x\times \frac{110}{100}\times \frac{110}{100}=36465-x$
$\Rightarrow \frac{121}{100}x=36465-x$

$\Rightarrow \frac{121}{100}x+x=36465$

$\Rightarrow \frac{221x}{100}=36465$

$\Rightarrow x=\frac{36465\times 100}{221}$
$\Rightarrow x=16500$
B's share =$36465-x=36465-16500=19965$
$\therefore$ A's share = Rs. 16500 and B's share = Rs. 19965