Loss at one price, gain at another — Aptitude Question
Loss at one price, gain at another: A man selling an article for ₹21 loses as much as he would gain by selling it… Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A man selling an article for ₹21 loses as much as he would gain by selling it for ₹33. What is the cost price?
Options
- ₹24
- ₹25
- ₹27
- ₹30
Show the answer and the worked solution
Correct answer: C. ₹27
Worked solution
- Loss at ₹21 = c − 21; gain at ₹33 = 33 − c.
- Equal, so c − 21 = 33 − c → 2c = 54 → c = ₹27.
- The cost is the midpoint of the two prices. ✓
Answer: ₹27.
The idea
When the loss at one price equals the gain at another, the cost price is exactly halfway between them. The average is the answer without any algebra.
Shortcut. Test the options for equal distances: only ₹27 sits 6 above ₹21 and 6 below ₹33; ₹24 (3 and 9) and ₹30 (9 and 3) are lopsided.
Common trap. "₹30" — a round figure just under the profitable ₹33 that feels right, but it makes the loss at ₹21 (₹9) three times the gain at ₹33 (₹3).