Question

Rs. $44,200$ are divided between Ram and John so that Ram's share at the end of $6$ years may be equal to John's share at the end of $4$ years, the rate of interest being $10$ percent compounded yearly. Find Ram's share

Answer 1

Let Ram's share be $=Rsx$
Then, John's share $=Rs44,200-x$

For Ram,
$N=6years$
$P=Rsx$
$R=10$ %

On interest being compounded, $Amount=P{(1+\frac{R}{100})}^N=x\times {(1+\frac{10}{100})}^6=x\times {\left(1.1\right)}^6$ -- (1)

For John,
$N=4years$
$P=Rs44,200-x$
$R=10$ %

On interest being compounded, $Amount=P{(1+\frac{R}{100})}^N=(44,200-x)\times {(1+\frac{10}{100})}^4=(44,200-x)\times {\left(1.1\right)}^4$ -- (2)

Given, eqn $1=$ eqn $2$
$=>x\times {\left(1.1\right)}^6=(44,200-x)\times {\left(1.1\right)}^4$
$=>x\times {\left(1.1\right)}^2=44,200-x$
$=>1.21x=44,200-x$
$=>2.21x=44,200$
$=>x=20,000$

Hence, Ram's share be $=Rsx=Rs20,000$
Then, John's share $=Rs44,200-x=Rs24,200$