Gopal divides ₹25,500 between his two grandsons, 14-year-old Akshay and…
2026
Gopal divides ₹25,500 between his two grandsons, 14-year-old Akshay and 15-year-old Atul. Each grandson will receive his share only on turning 21. Until then, each share earns interest at 4% per annum, compounded annually. Their amounts on turning 21 are equal. How much money did Gopal initially give to Atul?
Answer: C. 13,000 — ConceptUnder annual compounding, a principal P grows to A = P(1 + r)n after n years, where r is the annual interest rate. If two investments earn the same…
- A.
13,350
- B.
12,250
- C.
13,000
- D.
12,500
Attempted by 16 students.
Show answer & explanation
Correct answer: C
Concept
Under annual compounding, a principal P grows to A = P(1 + r)n after n years, where r is the annual interest rate.
If two investments earn the same rate and mature to equal amounts, but one remains invested for one extra year, the shorter-term principal must be (1 + r) times the longer-term principal.
Application
Akshay is 14, so his share grows for 7 years. Atul is 15, so his share grows for 6 years.
Let Akshay’s initial share be x and Atul’s initial share be y. Equal maturity amounts give x(1.04)7 = y(1.04)6.
Dividing both sides by (1.04)6 gives 1.04x = y.
The initial shares total ₹25,500, so x + y = 25,500. Substituting y = 1.04x gives 2.04x = 25,500, hence x = 12,500.
Therefore, y = 1.04 × 12,500 = 13,000.
Cross-check
The initial shares add to ₹25,500. Also, ₹12,500 × (1.04)7 and ₹13,000 × (1.04)6 are equal because ₹13,000 = ₹12,500 × 1.04.
Gopal initially gave Atul ₹13,000.