Principal from the CI–SI gap — Aptitude Question
Principal from the CI–SI gap: The difference between compound and simple interest for 2 years at 5% per annum is ₹50. Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
The difference between compound and simple interest for 2 years at 5% per annum is ₹50. What is the principal?
Options
- ₹15,000
- ₹18,000
- ₹20,000
- ₹25,000
Show the answer and the worked solution
Correct answer: C. ₹20,000
Worked solution
- P × (5/100)² = 50 → P × 0.0025 = 50.
- P = 50 ÷ 0.0025 = ₹20,000.
Answer: ₹20,000.
The idea
Rearranging P = difference × (100/r)² is one step. A small rate makes the gap tiny, so the principal comes out large.
Shortcut. At 5% the two-year gap is always P ÷ 400, since (1/20)² = 1/400, so P = 50 × 400. Check: ₹1,000 of first-year interest earns 5% = ₹50.
Common trap. ₹25,000 — writing 0.05² as 0.002 instead of 0.0025; 50 ÷ 0.002 gives exactly it.
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