Shivam has two grandsons Rupesh and Mandar. 12 year old Rupesh gets some money from Shivam’s wealth and 13 year old Mandar gets rest of the money. But Rupesh and Mandar will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 8% compounded annually. When both turn 23, they receive the same amount. How much had Shivam given Mandar (in ₹) initially, if total money with Shivam was ₹24700?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 12825.
Rupesh: 12 years old → will get money after 11 years
Mandar: 13 years old → will get money after 10 years
Let Rupesh’s amount = x
So, Mandar’s amount = 24700 − x
At 8% compound interest:
Final amount for Rupesh = x × (1.08)11
Final amount for Mandar = (24700 − x) × (1.08)10
Given: both final amounts are equal
x × (1.08)11 = (24700 − x) × (1.08)10
Divide both sides by (1.08)10:
x × 1.08 = 24700 − x
⇒ 1.08x + x = 24700
⇒ 2.08x = 24700
⇒ x = 24700 / 2.08 = ₹11,875 (Rupesh)
So, Mandar got: 24700 − 11875 = ₹12,825