Question

A sum of Rs. $69,300$ is to be divided between two boys $A$ and $B$, $21$ and $22$ years old respectively, in such a way that, if their portions be invested at $10$ per cent per annum compound interest, they will receive equal amounts on reaching $24$ years of age. What is the share of John in the original sum of money?

Answer 1

Let $A$'s share be $=$ Rs. $x$
Then, $B$'s share $=$ Rs. $69,300-x$
For $A$,
$N=24-21=3$ years
$P=$ Rs. $x$, $R=10\%$
On interest being compounded,

Amount $=P{(1+\frac{R}{100})}^N$

$=x\times {(1+\frac{10}{100})}^3$

$=x\times {\left(1.1\right)}^3$ ....(1)
For $B$,
$N=24-22=2$ years
$P=$ Rs. $69,300-x$, $R=10\%$
On interest being compounded,

Amount $=P{(1+\frac{R}{100})}^N$

$=(69,300-x)\times {(1+\frac{10}{100})}^2$

$=(69,300-x)\times {\left(1.1\right)}^2$ ....(2)
Given, eqn $1=$ eqn $2$
$\Rightarrow x\times {\left(1.1\right)}^3=(69,300-x)\times {\left(1.1\right)}^2$
$\Rightarrow x\times 1.1=69,300-x$
$\Rightarrow 2.1x=69,300$
$\Rightarrow x=33,000$
Hence, $A$'s share be $=$ Rs. $x=$ Rs. $33,000$
Then, John's share $=$ Rs. $69,300-x=$ Rs. $36,300$