Pramod has two grandsons Ashish and Ketan. 13 year old Ashish gets some money from Pramod’s wealth and 14 year old Ketan gets rest of the money. But Ashish and Ketan will get money only when they turn 24 years old. Till then the money is in a bank getting interest at rate 4% compounded annually. When both turn 24, they receive the same amount. How much had Pramod given Ketan (in Rs. ) initially, if total money with Pramod was Rs. 25500?

Correct option is B

Given:
Total amount = ₹25,500
Rate of compound interest = 4% per annum
Ashish’s present age = 13 years
Ketan’s present age = 14 years
Both will receive the money at age 24 → Ashish invests for 11 years and Ketan for 10 years
Both receive the same final amount
Formula Used:
$$A = P \times \left(1 + \frac{R}{100}\right)^{T}$$​​
Solution:
Let Ashish’s initial amount = P₁ and Ketan’s initial amount = P₂
P₁ + P₂ = 25,500 ...(i)
Final amounts are equal:
P₁ × (1.04)11 = P₂ × (1.04)10
P₁ × 1.04 = P₂
P₂ = 1.04P₁
Substitute in (i): P₁ + 1.04P₁ = 25,500
2.04P₁ = 25,500
P₁ = 25,500 ÷ 2.04 = 12,500
P₂ = 1.04 × 12,500 = 13,000