Mohan has two grandsons, Pramod and Ashish. 16-year-old Pramod gets some money…
2026
Mohan has two grandsons, Pramod and Ashish. 16-year-old Pramod gets some money from Mohan's wealth and 17-year-old Ashish gets the rest of the money. But Pramod and Ashish will get the money only when they turn 25 years old. Till then the money will be kept in a bank earning interest at the rate of 10% per annum, compounded annually. When both turn 25, they receive the same amount. How much money (in ₹) had Mohan initially given Ashish, if the total money Mohan had was ₹25,200?
Answer: B. 13,200 — Concept: money left at compound interest grows by the same factor every year. If r is the annual rate written as a decimal — so 10% per annum means r = 0.1 —…
- A.
13,550
- B.
13,200
- C.
11,750
- D.
12,000
Attempted by 18 students.
Show answer & explanation
Correct answer: B
Concept: money left at compound interest grows by the same factor every year. If r is the annual rate written as a decimal — so 10% per annum means r = 0.1 — a principal P becomes P(1 + r)n after n years, so a maturity value is fixed by two things only: the principal and the number of years it stays invested. If two unequal principals must mature to the same amount, they have to be inversely proportional to their growth factors: the sum that stays invested for fewer years must start out larger, and each extra year of compounding is worth exactly one extra factor of (1 + r).
Application to this problem:
Pramod is 16 today and receives his money at 25, so his share stays invested for 25 − 16 = 9 years.
Ashish is 17 today, so his share stays invested for 25 − 17 = 8 years.
Let Ashish's share be A and Pramod's share be P. The whole corpus is split between the two boys, so A + P = ₹25,200.
Both must receive the same amount at 25, and the rate is 10% per annum, so (1 + r) = 1.1 and the equal-maturity condition is P(1.1)9 = A(1.1)8.
Divide both sides by (1.1)8, the factor common to the two sides: 1.1P = A, that is, A = 11P/10.
Substitute this into the total: P + 11P/10 = 25,200, so 21P/10 = 25,200 and P = 25,200 × 10/21 = ₹12,000.
Hence A = ₹25,200 − ₹12,000 = ₹13,200, which is the money Mohan initially gave Ashish.
Cross-check: work out what each boy actually holds at 25.
Grandson | Age now | Years invested | Share (₹) | Amount at 25 |
|---|---|---|---|---|
Pramod | 16 | 9 | 12,000 | 12,000 × (1.1)9 |
Ashish | 17 | 8 | 13,200 | 13,200 × (1.1)8 = 12,000 × (1.1)9 |
Ashish's ₹13,200 × (1.1)8 = ₹12,000 × 1.1 × (1.1)8 = ₹12,000 × (1.1)9, which is exactly what Pramod's ₹12,000 grows to. Both therefore receive the same amount at 25, as the question demands.
Contrast: the two shares must stand in the ratio 11 : 10 in favour of Ashish, because his money loses one year of compounding relative to Pramod's and one year at 10% multiplies a sum by 1.1. An equal split, or any split that favours the younger grandson, would leave the two boys holding different amounts at 25.