UPSC Prelims 2002 Q10: Science & Technology – Quantitative Aptitude
A trader fixed the price of an article in such a way that by giving a rebate of 10 % on the
price fixed he made a profit of 15 %. If the cost of the article is Rs 72, the price fixed on it is
- (a) Rs 82.80
- (b) Rs 90.00
- (c) Rs 92.00
- (d) Rs 97.80
Answer: (c) Rs 92.00
Explanation
Marked price when a 10% rebate still gives a 15% profit
| Step | Value |
|---|---|
| Cost price | Rs 72 |
| Selling price with 15% profit | 72 × 1.15 = Rs 82.80 |
| Selling price after 10% rebate | 0.9 × fixed price |
| Fixed price | 82.80 ÷ 0.9 = Rs 92.00 |
After the rebate of 10 per cent the trader sells at 90 per cent of the fixed price, and that equals the selling price giving a profit of 15 per cent. So 0.9 × P = 82.80 and the price fixed is Rs 92.
Answer: (c) Rs 92.00.
Why each option is right or wrong
- (a) Incorrect. Rs 82.80 is the selling price after the rebate, not the price fixed.
- (b) Incorrect. Rs 90 less 10% gives Rs 81, a profit of 12.5% on Rs 72.
- (c) CORRECT. 92 × 0.9 = 82.80, which is 15% above Rs 72.
- (d) Incorrect. Rs 97.80 less 10% gives Rs 88.02, a profit above 22%.
Key point
Selling price = cost × (1 + profit%) = marked price × (1 − discount%).
Remember
Marked price = cost × 1.15 ÷ 0.9.
Common mistakes
- Choosing Rs 82.80, which is the selling price rather than the price fixed.
- Adding 10% to 82.80 instead of dividing by 0.9.
- Taking the profit on the marked price instead of on cost.
Exam tip
Test the options: 92 × 0.9 = 82.8 = 72 × 1.15.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Profit and Loss)