Same sum, two periods — Aptitude Question
Same sum, two periods: The simple interest on a sum for 3 years at 8% exceeds that for 2 years at 5% by ₹280. Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 90 seconds
Question
The simple interest on a sum for 3 years at 8% exceeds that for 2 years at 5% by ₹280. What is the sum?
Options
- ₹2,000
- ₹2,400
- ₹2,800
- ₹3,000
Show the answer and the worked solution
Correct answer: A. ₹2,000
Worked solution
- First: P × 8 × 3/100 = 0.24P. Second: P × 5 × 2/100 = 0.10P.
- Difference = 0.14P = 280.
- P = ₹2,000.
Answer: ₹2,000.
The idea
Convert each interest to a percentage of the same principal, subtract, and solve once. The principal never has to be split.
Shortcut. 24% − 10% = 14% of P is ₹280, so 1% is ₹20 and P is ₹2,000. Back-check: ₹480 − ₹200 = ₹280.
Common trap. ₹2,800 echoes the ₹280 and looks right if the gap is taken as 10% of the sum; the actual gap is 24% − 10% = 14%, which on ₹2,800 would be ₹392.
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