Same selling price, one gain and one loss — Aptitude
Same selling price, one gain and one loss: Two articles are each sold for ₹1,200 — one at a 20% profit, the other… Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Two articles are each sold for ₹1,200 — one at a 20% profit, the other at a 20% loss. Overall, the seller makes:
Options
- 4% loss
- 2% loss
- No profit, no loss
- 4% profit
Show the answer and the worked solution
Correct answer: A. 4% loss
Worked solution
- CP of the first = 1200 ÷ 1.2 = 1,000. CP of the second = 1200 ÷ 0.8 = 1,500.
- Total CP = 2,500; total SP = 2,400.
- Loss = 100 on 2,500 = 4% loss.
Answer: 4% loss.
The idea
When two items sell at the same price with an equal x% gain and x% loss, the result is always a loss of x²/100 percent. Here 20²/100 = 4%.
Shortcut. The loss-making article cost more (₹1,500 against ₹1,000), so the loss outweighs the gain, ruling out break-even and any profit; the loss is 100 on 2,500 = 4%.
Common trap. No profit, no loss — assuming an equal 20% gain and 20% loss cancel; the percentages are on different cost prices.