The three-year gap — Aptitude Question
The three-year gap: The difference between compound and simple interest on a sum for 3 years at 10% per annum is ₹93. Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
The difference between compound and simple interest on a sum for 3 years at 10% per annum is ₹93. What is the sum?
Options
- ₹2,500
- ₹3,000
- ₹3,500
- ₹4,000
Show the answer and the worked solution
Correct answer: B. ₹3,000
Worked solution
- Difference for 3 years = P(r/100)²(3 + r/100) = P × 0.01 × 3.1 = 0.031P.
- 0.031P = 93 → P = ₹3,000.
- Check: CI = 3,000 × 1.331 − 3,000 = 993; SI = 900; difference 93. ✓
Answer: ₹3,000.
The idea
Learn both gap formulas: two years is P(r/100)² and three years is P(r/100)²(3 + r/100). Verifying against the full calculation once builds trust in them.
Shortcut. At 10%, every ₹1,000 has a three-year gap of ₹31 (1,331 − 1,300), so ₹93 = 3 × 31 means ₹3,000.
Common trap. ₹3,500 or ₹4,000 tempt a solver who guesses from the size of the gap; at ₹31 per ₹1,000 they would give ₹108.50 and ₹124, not ₹93.
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