A sum split into two investments — Aptitude Question
A sum split into two investments: ₹2,600 is split into two parts, one lent at 10% and the other at 8% simple… Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
₹2,600 is split into two parts, one lent at 10% and the other at 8% simple interest for one year. If the total interest is ₹230, what is the part lent at 10%?
Options
- ₹1,000
- ₹1,100
- ₹1,200
- ₹1,400
Show the answer and the worked solution
Correct answer: B. ₹1,100
Worked solution
- 0.10x + 0.08(2,600 − x) = 230.
- 0.10x + 208 − 0.08x = 230 → 0.02x = 22.
- x = ₹1,100.
- Check: 110 + 0.08 × 1,500 = 110 + 120 = 230. ✓
Answer: ₹1,100.
The idea
One variable for one part, the remainder for the other, then one equation on the total interest. Alligation also works: the average rate is 230/2,600 ≈ 8.85%.
Shortcut. At 8% on all ₹2,600 the interest would be ₹208; the extra ₹22 comes from the 2% gap on the 10% part, so that part is 22 ÷ 0.02 = ₹1,100.
Common trap. ₹1,000 — it gives ₹100 + ₹128 = ₹228, close enough to ₹230 that a rough check passes it; the missing ₹2 needs another ₹100 at the 2% gap.
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