Two horses at the same price — Aptitude Question
Two horses at the same price: A man sold two horses for ₹1,955 each, gaining 15% on one and losing 15% on the other. Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
A man sold two horses for ₹1,955 each, gaining 15% on one and losing 15% on the other. What was his overall loss percent?
Options
- 1.5%
- 2.25%
- 3%
- No loss
Show the answer and the worked solution
Correct answer: B. 2.25%
Worked solution
- CP of the first = 1955 / 1.15 = ₹1,700; CP of the second = 1955 / 0.85 = ₹2,300.
- Total CP = ₹4,000; total SP = ₹3,910.
- Loss = 90 on 4,000 = 2.25%.
- This matches the shortcut 15²/100 = 2.25. ✓
Answer: 2.25%.
The idea
Same selling price, equal gain and loss of x% — the result is always a loss of x²/100 percent, whatever the price. The intuition: the loss is taken on a larger cost than the gain.
Shortcut. Loss = (x/10)² % with x = 15, i.e. 1.5² = 2.25%. The ₹1,955 price never enters, so both cost-price divisions can be skipped.
Common trap. "No loss" — assuming a 15% gain and a 15% loss cancel; the loss falls on the dearer horse (cost ₹2,300) and outweighs the gain on the ₹1,700 one.