Mandar has two grandsons, Ketan and Tushar. 13-year-old Ketan gets some money…
2026
Mandar has two grandsons, Ketan and Tushar. 13-year-old Ketan gets some money from Mandar’s wealth, and 14-year-old Tushar gets the rest of the money. But Ketan and Tushar will get the money only when they turn 24 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 24, they receive the same amount. If the total money Mandar had was ₹23,100, how much money (in ₹) did Mandar initially give to Tushar?
Answer: A. 12,100 — Concept: A principal P compounded annually at r% per annum for n years grows to A = P(1 + r/100)n. When two different principals must grow to the SAME…
- A.
12,100
- B.
10,750
- C.
11,000
- D.
12,450
Attempted by 15 students.
Show answer & explanation
Correct answer: A
Concept: A principal P compounded annually at r% per annum for n years grows to A = P(1 + r/100)n. When two different principals must grow to the SAME maturity amount, dividing their two growth equations cancels the common years: the money that stays invested for FEWER years must start out larger, and the two principals stand in the ratio (1 + r/100) raised to the difference between their investment periods.
Application to this problem
Investment periods: Ketan is 13, so his money compounds for 24 − 13 = 11 years; Tushar is 14, so his money compounds for 24 − 14 = 10 years.
Let Ketan’s share be K and Tushar’s share be T. The whole fund is divided, so K + T = 23,100.
Equal maturity amount: K × (1.1)11 = T × (1.1)10.
Divide both sides by (1.1)10: 1.1 K = T, that is T = 11K/10. So the shares are in the ratio K : T = 10 : 11 — the younger grandson, whose money grows for one extra year, starts with the smaller share.
Substitute into the total: K + 11K/10 = 23,100 → 21K/10 = 23,100 → K = 23,100 × 10/21 = 11,000.
Therefore T = 23,100 − 11,000 = 12,100.
Cross-check: 11,000 × (1.1)11 = 11,000 × 1.1 × (1.1)10 = 12,100 × (1.1)10. Both maturity values are identical (about ₹31,384 each), so the “same amount at age 24” condition is satisfied.
Ratio shortcut: Once the split is known to be 10 : 11, divide the fund into 10 + 11 = 21 parts: 23,100 ÷ 21 = 1,100 per part, so the 11-part share is 11 × 1,100.
Result: Mandar initially gave Tushar ₹12,100.