Shivam has two grandsons, Rupesh and Mandar. 12-year-old Rupesh gets some…
2026
Shivam has two grandsons, Rupesh and Mandar. 12-year-old Rupesh gets some money from Shivam’s wealth, and 13-year-old Mandar gets the rest of the money. But Rupesh and Mandar 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 8% per annum, compounded annually. When both turn 25, they receive the same amount. If the total amount Shivam had was ₹23,400, how much money (in ₹) did Shivam initially give to Mandar?
Answer: B. 12,150 — Concept Under annual compounding at rate r, a principal P becomes P(1 + r)n after n years. If two different principals must reach the same maturity value…
- A.
12,500
- B.
12,150
- C.
11,250
- D.
11,000
Attempted by 25 students.
Show answer & explanation
Correct answer: B
Concept
Under annual compounding at rate r, a principal P becomes P(1 + r)n after n years. If two different principals must reach the same maturity value while staying invested for different numbers of years, they are tied by P1(1 + r)n₁ = P2(1 + r)n₂, so P1/P2 = (1 + r)n₂ − n₁. The money that stays invested for fewer years must therefore start out larger — by exactly one growth factor (1 + r) for each extra year the other one is invested.
Applying it here
Each share stays in the bank until that grandson turns 25. Rupesh is 12, so his share compounds for 25 − 12 = 13 years; Mandar is 13, so his share compounds for 25 − 13 = 12 years.
Let Rupesh’s share be R and Mandar’s share be M. Between them they take the whole estate, so R + M = 23,400.
Both must mature to the same amount at 8% per annum, i.e. R(1.08)13 = M(1.08)12.
Twelve years of growth are common to both, so divide each side by (1.08)12: 1.08 R = M, that is M = 27R/25.
Substitute into the total: R + 27R/25 = 23,400, so 52R/25 = 23,400 and R = 23,400 × 25 / 52 = 11,250.
Therefore M = 23,400 − 11,250 = 12,150, so ₹12,150 is the amount Shivam initially set aside for Mandar.
Cross-check
11,250 + 12,150 = 23,400, so the estate is fully accounted for.
12,150 ÷ 11,250 = 1.08 exactly — one single extra year of 8% growth, which is precisely what Rupesh’s longer wait has to supply.
Both mature to the same figure: 11,250 × (1.08)13 = 12,150 × (1.08)12 ≈ ₹30,596.
Note the age trap: the younger grandson waits longer, so his money compounds for more years and his starting share is the smaller of the two.