Gain on one, loss on the other — Aptitude Question
Gain on one, loss on the other: Two articles are bought for a total of ₹900. One is sold at a 20% profit and the… Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
Two articles are bought for a total of ₹900. One is sold at a 20% profit and the other at a 10% loss, and there is no overall gain or loss. What was the cost of the article sold at a profit?
Options
- ₹300
- ₹360
- ₹450
- ₹600
Show the answer and the worked solution
Correct answer: A. ₹300
Worked solution
- Let the first article cost ₹x, the second ₹(900 − x).
- Profit = 0.20x, loss = 0.10(900 − x), and these cancel.
- 0.20x = 90 − 0.10x → 0.30x = 90 → x = ₹300.
- Check: profit 60 on ₹300, loss 60 on ₹600. ✓
Answer: ₹300.
The idea
Set the rupee profit equal to the rupee loss, not the percentages. The article with the higher rate always turns out to be the cheaper one.
Shortcut. Alligation: the rates +20% and −10% balance at 0 when the costs are in the ratio 10 : 20 = 1 : 2, so the profit article cost 1/3 of ₹900 = ₹300.
Common trap. "₹600" — getting the 1 : 2 split right but giving the larger share to the article sold at a profit; the higher rate goes with the smaller cost.