Mukund has two grandsons Sachin and Chetan. 13 year old Sachin gets some money from Mukund’s wealth and 14 year old Chetan gets rest of the money. But Sachin and Chetan will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 10% compounded annually. When both turn 23, they receive the same amount. How much had Mukund given Chetan (in ₹) initially, if total money with Mukund was ₹25200?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 13200.
Let Sachin’s initial share = S
Chetan’s initial share = 25200 − S
Sachin’s money grows for 23 − 13 = 10 years
Chetan’s money grows for 23 − 14 = 9 years
At age 23:
Sachin’s amount = S × (1 + 10/100)10 = S × (1.1)10
Chetan’s amount = (25200 − S) × (1.1)9
Given both amounts equal:
S × (1.1)10 = (25200 − S) × (1.1)9
S × 1.1 = 25200 − S
1.1S + S = 25200
2.1S = 25200
S = 25200 / 2.1 = 12000
Chetan’s initial share = 25200 − 12000 = 13200