Ketan has two grandsons, Mahesh and David. 15-year-old Mahesh gets some money from Ketan’s wealth, and 16-year-old David gets the 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 a rate of 10% compounded annually. When both turn 22, they receive the same amount. How much had Ketan given David (in Rs.) initially if the total money with Ketan was Rs. 25200?

Correct option is D

Given:
Total money = ₹25200
Mahesh's current age = 15 years
David's current age = 16 years
Age to receive money = 22 years
Interest rate (r) = 10% compounded annually
Amount received by Mahesh = Amount received by David
Formula Used:
​$$A = P \times \left(1 + \frac{r}{100}\right)^n$$​​
Where n is the number of years.
Solution:
Let Mahesh's initial share be M and David's initial share be D
M + D = ₹25200......(1)
Mahesh's receiving time = 22 - 15 = 7 years
David's receiving time = 22 - 16 = 6 years
Amount received by Mahesh = $$M \times \left(1 + \frac{10}{100}\right)^7 = M \times (1.1)^7$$​​

Amount received by David = $$D \times \left(1 + \frac{10}{100}\right)^6 = D \times (1.1)^6$$​​
Given that they receive the same amount:
​$$M × (1.1)^7 = D × (1.1)^6$$​​
=> M × 1.1 = D
Substitute D in the first equation:
=> M + 1.1M =₹25200
=> 2.1 M= ₹25200
=> M = 12000
M + D =₹25200 
D = ₹25200  - 12000 = 13200