Rodney has two grandsons Amit and Gopal. 11 year old Amit gets some money from Rodney’s wealth and 12 year old Gopal gets rest of the money. But Amit and Gopal 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 Rodney given Gopal (in Rs. ) initially, if total money with Rodney was Rs. 23100?

Correct option is C

Given:
Total amount = ₹23,100
Rate of compound interest = 10% per annum
Amit’s present age = 11 years
Gopal’s present age = 12 years
Both will receive the money at age 23 → Amit invests for 12 years and Gopal for 11 years
Both receive the same final amount
Formula Used:
​$$\text{Compound Amount } (A) = P \times \left(1 + \frac{R}{100}\right)^T$$​​
Solution:
Let Amit’s initial amount = P₁ and Gopal’s initial amount = P₂
P₁ + P₂ = 23,100 ...(i)
 Final amounts are equal:
​$$P₁ × (1.1)^{12} = P₂ × (1.1)^{11}$$​​
=> P₁ × 1.1 = P₂
=> P₂ = 1.1P₁
Substitute in (i): P₁ + 1.1P₁ = 23,100
2.1P₁ = 23,100
P₁ = 23,100 ÷ 2.1 = 11,000
P₂ = 1.1 × 11,000 = 12,100