Two amounts under simple interest — Aptitude Question
Two amounts under simple interest: A sum amounts to ₹1,560 in 3 years and ₹1,680 in 5 years at simple interest. Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A sum amounts to ₹1,560 in 3 years and ₹1,680 in 5 years at simple interest. What is the principal?
Options
- ₹1,200
- ₹1,320
- ₹1,380
- ₹1,440
Show the answer and the worked solution
Correct answer: C. ₹1,380
Worked solution
- Interest for 2 years = 1,680 − 1,560 = ₹120, so one year's interest = ₹60.
- Interest for 3 years = ₹180.
- Principal = 1,560 − 180 = ₹1,380.
Answer: ₹1,380.
The idea
Under simple interest each year adds the same amount, so the difference between two amounts gives the annual interest directly. Subtract back to reach the principal.
Shortcut. Extrapolate back in one line: P = (5 × 1,560 − 3 × 1,680) ÷ (5 − 3) = (7,800 − 5,040) ÷ 2 = ₹1,380.
Common trap. ₹1,440 — subtracting the ₹120 difference once from ₹1,560; that ₹120 covers two years, so three years of interest is ₹180.
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