Mandar has two grandsons Ketan and Tushar. 11 year old Ketan gets some money from Mandar's wealth and 12 year old Tushar gets rest of the money. But Ketan and Tushar will get money only when they turn 22 years old. Till then the money is in a bank getting interest at rate 8% compounded annually. When both turn 22, they receive the same amount. How much had Mandar given Tushar (in ₹) initially, if total money with Mandar was ₹24700?

Given:

Total money = ₹24700

Ketan's current age = 11 years

Tushar's current age = 12 years

Age to receive money = 22 years

Interest rate (r) = 8% compounded annually

Amount received by Ketan = Amount received by Tushar

Formula Used:

Amount (A) = Principal (P) × (1 + r/100)ⁿ

Where n is the number of years.

Calculation:

Let Ketan's initial share be K and Tushar's initial share be T.

K + T = 24700

Ketan's receiving time = 22 - 11 = 11 years

Tushar's receiving time = 22 - 12 = 10 years

Amount received by Ketan = K × (1 + 8/100)¹¹ = K × (1.08)¹¹

Amount received by Tushar = T × (1 + 8/100)¹⁰ = T × (1.08)¹⁰

Given that they receive the same amount:

⇒ K × (1.08)¹¹ = T × (1.08)¹⁰

⇒ K × 1.08 = T

Substitute T in the first equation:

⇒ K + 1.08K = 24700

⇒ 2.08K = 24700

⇒ K = 24700 / 2.08

⇒ K = 11875

Now find T:

T = 24700 - K

⇒ T = 24700 - 11875

⇒ T = 12825

∴ Mandar had given Tushar ₹12825 initially.