Mukund has two grandsons Sachin and Chetan. 13 year old Sachin gets some money from Mukund’s wealth and 14 year old Chetan gets rest of the money. But Sachin and Chetan will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 10% compounded annually. When both turn 23, they receive the same amount. How much had Mukund given Chetan (in Rs. ) initially, if total money with Mukund was Rs. 25200?

Correct option is C

Given:
Total money = Rs. 25,200
Rate of interest = 10% per annum (Compound Interest)
Age of Sachin = 13 years
Age of Chetan = 14 years
Age at which money is received = 23 years
Time period for Sachin = 23 − 13 = 10 years
Time period for Chetan = 23 − 14 = 9 years
Formula Used:
​$$\text {Amount} = \text{Principal }(1 + \frac{R}{100})^T$$​​
Solution:
Let money given to Sachin = x
Money given to Chetan = 25,200 − x
Since final amounts are equal:
​$$x(1.1)^10 = (25,200 − x)(1.1)^9$$​​
Dividing both sides by $$(1.1)^9$$​:
1.1x = 25,200 − x
2.1x = 25,200
x = 12,000
Money given to Chetan:
25,200 − 12,000 = 13,200