Pramod has two grandsons, Ashish and Ketan. Ashish is 13 years old and Ketan…
2026
Pramod has two grandsons, Ashish and Ketan. Ashish is 13 years old and Ketan is 14 years old. Pramod divides ₹23,400 between them. Each grandson will receive his share only when he turns 24; until then, the money earns 8% interest per annum, compounded annually. If both receive the same maturity amount at age 24, how much did Pramod initially give to Ketan?
Answer: B. 12,150 — ConceptUnder annual compound interest, a principal P invested for n years at rate r grows to P(1 + r)n. When two investments must reach the same maturity…
- A.
11,000
- B.
12,150
- C.
12,500
- D.
11,250
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Concept
Under annual compound interest, a principal P invested for n years at rate r grows to P(1 + r)n.
When two investments must reach the same maturity value but one remains invested for one extra year, the shorter-term principal must be (1 + r) times the longer-term principal.
Application
Let Ashish’s initial share be A and Ketan’s initial share be K. Since their ages are 13 and 14, the money remains invested for 11 years and 10 years, respectively.
Equal maturity amounts give A(1.08)11 = K(1.08)10.
Dividing both sides by (1.08)10 gives 1.08A = K.
The initial shares total ₹23,400, so A + K = 23,400. Substituting K = 1.08A gives 2.08A = 23,400.
Therefore A = 23,400 ÷ 2.08 = ₹11,250, and K = 1.08 × 11,250 = ₹12,150.
Cross-check
Ashish’s amount at age 24 is 11,250(1.08)11, while Ketan’s is 12,150(1.08)10 = 11,250(1.08)11. The maturity amounts are equal and the initial shares add to ₹23,400.
Result
Thus, Pramod initially gave Ketan ₹12,150.