Atul has two grandsons Baban and Rakesh. 11 year old Baban gets some money from Atul’s wealth and 12 year old Rakesh gets rest of the money. But Baban and Rakesh will get money only when they turn 24 years old. Till then the money is in a bank getting interest at rate 5% compounded annually. When both turn 24, they receive the same amount. How much had Atul given Rakesh (in Rs. ) initially, if total money with Atul was Rs. 24600?

Correct option is A

Given:
Total money = 24600
Baban is 11 years old → will receive money at 24 → time = 13 years
Rakesh is 12 years old → will receive money at 24 → time = 12 years
Rate = 5% compounded annually
Both receive the same amount at age 24
Formula Used:
Amount = Principal × $$(1.05)^\text{time}$$​​
If $$A_B = A_R$$​, then: Baban’s principal × $$1.05^{13}$$​= Rakesh’s principal ×$$1.05^{12}$$​
Solution:
Let Baban’s principal = x
Let Rakesh’s principal = y
=> x + y = 24600
​$$=> x × 1.05^{13} = y × 1.05^{12}$$​​
=> x × 1.05 = y
Substitute x = y ÷ 1.05 in total:
=> y ÷ 1.05 + y = 24600
=> y(1 + $$\frac{1}{1.05}$$​) = 24600
=> 1 + 0.95238 = 1.95238
=> y × 1.95238 = 24600
=> y = 24600 ÷ 1.95238
=> y = 12600