Baban has two grandsons Rakesh and Shivam. 13 year old Rakesh gets some money from Baban’s wealth and 14 year old Shivam gets rest of the money. But Rakesh and Shivam will get money only when they turn 22 years old. Till then the money is in a bank getting interest at rate 5% compounded annually. When both turn 22, they receive the same amount. How much had Baban given Shivam (in Rs. ) initially, if total money with Baban was Rs. 24600?

Correct option is A

Given:
Total money with Baban = Rs. 24600
Rate of interest = 5% compounded annually
Rakesh is 13 years old, Shivam is 14 years old.
Both will receive the same amount when they turn 22 years old, after the money grows with compound interest.
Formula Used:
​$$A = P \times \left(1 + \frac{r}{100}\right)^t$$​​
Where: A = Amount after interest, P = Principal, r = Interest rate, t = Time period
Solution:
Let the amount given to Rakesh initially be P_R and the amount given to Shivam initially be P_S.
For Rakesh, the amount will grow for 9 years (since he is 13 now and will be 22 when he receives the money).
For Shivam, the amount will grow for 8 years (since he is 14 now and will be 22 when he receives the money).
​$$P_R \times \left(1 + \frac{5}{100}\right)^9 = P_S \times \left(1 + \frac{5}{100}\right)^8 \\P_R \times 1.05 = P_S$$​​
Substitute P_R into the total amount equation: 
​$$P_R + P_S = 24600\\P_R + P_R \times 1.05 = 24600\\P_R \times 2.05 = 24600\\P_R = \frac{24600}{2.05} = 12000\\P_S = 24600 - 12000 = 12600\\$$​​
The amount Baban initially gave to Shivam is Rs. 12600.