Ketan has two grandsons Mahesh and David. 15 year old Mahesh gets some money from Ketan’s wealth and 16 year old David gets rest of the money. But Mahesh and David will get money only when they turn 22 years old. Till then the money is in a bank getting interest at rate 10% compounded annually. When both turn 22, they receive the same amount. How much had Ketan given David (in ₹) initially, if total money with Ketan was ₹25200? 

Given:

Total money with Ketan = ₹25200

Age of Mahesh = 15 years

Age of David = 16 years

Interest rate = 10% compounded annually

Both Mahesh and David will receive money when they turn 22 years old, and they both receive the same amount.

Formula Used:

Compound Interest Formula: Final Amount (A) = Principal (P) × (1 + Rate/100)^Time

Calculation:

Let the initial amount given to Mahesh be x, and the initial amount given to David be 25200 - x.

Mahesh's money grows for (22 - 15) = 7 years:

Final Amount for Mahesh = x × (1 + 10/100)⁷

Final Amount for Mahesh = x × (1.1)⁷

Final Amount for Mahesh = x × 1.9487171

David's money grows for (22 - 16) = 6 years:

Final Amount for David = (25200 - x) × (1 + 10/100)⁶

Final Amount for David = (25200 - x) × (1.1)⁶

Final Amount for David = (25200 - x) × 1.771561

Since both receive the same amount:

x × 1.9487171 = (25200 - x) × 1.771561

Expanding the equation:

⇒ 1.9487171x = 25200 × 1.771561 - x × 1.771561

⇒ 1.9487171x + 1.771561x = 25200 × 1.771561

⇒ 3.7202781x = 44646.2232

⇒ x = 44646.2232 / 3.7202781

⇒ x ≈ 12000

Initial amount given to David = 25200 - x = 25200 - 12000 = ₹13200

The correct answer is ₹13200.