David has two grandsons Rodney and Amit. 15 year old Rodney gets some money from David’s wealth and 16 year old Amit gets rest of the money. But Rodney and Amit will get money only when they turn 22 years old. Till then the money is in a bank getting interest at rate 8% compounded annually. When both turn 22, they receive the same amount. How much had David given Amit (in Rs. ) initially, if total money with David was Rs. 23400?

Correct option is A

Given:
Total money = Rs. 23400
Rodney is 15 years old and will receive money after 7 years
Amit is 16 years old and will receive money after 6 years
Rate of compound interest = 8% per annum
Both will receive equal amount at the age of 22
Formula Used:
Amount = Principal $$\left(1 + \frac{r}{100}\right)^t$$​
Solution:
Let Rodney's initial amount = R
Then Amit's initial amount = 23400 - R
Rodney's Amount after 7 years = Amit's Amount after 6 years
​$$R\left(1 + \frac{8}{100}\right)^7 = A\left(1 + \frac{8}{100}\right)^6\\[10pt]R(1.08)^7 = (23400 - R)(1.08)^6\\[10pt]\frac{R(1.08)^7}{(1.08)^6} = 23400 - R\\[10pt]R(1.08) = 23400 - R\\[10pt]1.08R + R = 23400\\[10pt]2.08R = 23400\\[10pt]R = \frac{23400}{2.08} = 11250$$​​
Amit's share= 23400 - 11250 = 12150