Divide ₹ 28730 between A and B so that when their shares are lent out at 10 per cent compound interest compounded per year, the amount that A receives in 3 years is same as what B receives in 5 years.

Let share of A = ₹ x and share of B = ₹ 28730 - ₹ x.

For A :

P = ₹ x

r = 10%

n = 3 years

By formula,

Amount = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Substituting values we get :

$\Rightarrow \text{Amount } = x\Big(1 + \dfrac{10}{100}\Big)^3 \\[1em] = x \times \Big(\dfrac{110}{100}\Big)^3\\[1em] = x \times \Big(\dfrac{11}{10}\Big)^3$

For B :

P = ₹ (28730 - x)

r = 10%

n = 5 years

By formula,

Amount = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Substituting values we get :

$\Rightarrow \text{Amount } = (28730 - x) \times \Big(1 + \dfrac{10}{100}\Big)^5 \\[1em] = (28730 - x) \times \Big(\dfrac{110}{100}\Big)^5 \\[1em] = (28730 - x) \times \Big(\dfrac{11}{10}\Big)^5$

Since, amount received by A and B are equal.

$\therefore x \times \Big(\dfrac{11}{10}\Big)^3 = (28730 - x) \times \Big(\dfrac{11}{10}\Big)^5 \\[1em] \Rightarrow x = (28730 - x) \times \Big(\dfrac{11}{10}\Big)^2 \\[1em] \Rightarrow x = (28730 - x) \times \dfrac{121}{100} \\[1em] \Rightarrow 100x = 121(28730 - x) \\[1em] \Rightarrow 100x = 3476330 - 121x \\[1em] \Rightarrow 100x + 121x = 3476330 \\[1em] \Rightarrow 221x = 3476330 \\[1em] \Rightarrow x = \dfrac{3476330}{221} \\[1em] \Rightarrow x = 15730.$

₹ (28730 - x) = ₹ (28730 - 15730) = ₹ 13000.

Hence, share of A and B are ₹ 15730 and ₹ 13000 respectively.