Question

A sum of ₹ 69,300 is to be divided between two friends Mahesh and Suresh. They are 11 and 12 years old respectively. Their respective portions are compounded annually at 10% per annum. They will get the same amount when they are 24 years old. Find the share of Suresh.

Answer 1

Let the share of Mahesh be $x$.

Share of Suresh = ₹$(69,300-x)$
Amount received by Mahesh after 13 years(when she will turn 24) = $x(1+\frac{10}{100}{)}^{13}$

Amount received by Suresh after 12 years(when she will turn 24) = $(69,300-x)(1+\frac{10}{100}{)}^{12}$

As per the question, both of them will get the same amount of money.

So, $x(1+\frac{10}{100}{)}^{13}$ $=$ $(69,300-x)(1+\frac{10}{100}{)}^{12}$

⇒ $x(1+\frac{10}{100})=(69,300-x)$

⇒ $\frac{110x}{100}=69,300-x$

⇒ $\frac{210x}{100}=69,300$

⇒ $x=₹33,000$

So, share of Mahesh = ₹33,000

Share of Suresh = ₹(69,300- 33,000) = ₹36,300