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 10% 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. 23100?

Correct option is B

Given:

Total money with Baban = Rs. 23100
Rate of interest = 10% compounded annually
Rakesh is 13 years old, Shivam is 14 years old.
Both will receive the same amount at age 22, after the money grows with compound interest.
Formula Used:
​$$A = P \left(1 + \frac{r}{100}\right)^t$$​​
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.
After the interest is applied, both will receive the same amount when they turn 22.
Now, applying the compound interest formula for both:
​$$P_R \cdot (1.1)^9 = P_S \cdot (1.1)^8\\P_R \cdot (1.1) = P_S$$​​
Since the total amount is Rs. 23100, we also have the equation:
​$$P_R + P_S = 23100\\P_R + P_R \cdot (1.1) = 23100\\P_R = 11000\\\text{We know}\\P_R \cdot 1.1 = P_S\\P_S = 11000 \times 1.1 = 12100\\$$​​
Thus, the amount given to Shivam initially was Rs. 12100.