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 ₹) initially, if total money with Atul was ₹24600?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 12600.
Let the initial amounts be: Baban = x and Rakesh = 24600 − x
Baban: age 11 → will get money at 24 → 13 years investment
Rakesh: age 12 → will get money at 24 → 12 years investment
At maturity, both amounts are equal = x × (1.05)13 = (24600 − x) × (1.05)12
⇒ x × 1.05 = 24600 − x
⇒ 1.05x + x = 24600
⇒ 2.05x = 24600
⇒ x = 12000
So Rakesh got = 24600 − 12000 = ₹12,600