UPSC Prelims 2008 Q5: Science & Technology – Quantitative Aptitude
A person purchases 100 pens at a discount of 10%. The net amount of money spent by the
person to purchase the pens is Rs 600. The selling expenses incurred by the person are 15% on
the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%?
- (a) Rs 802·50
- (b) Rs 811·25
- (c) Rs 862·50
- (d) Rs 875
Answer: (c) Rs 862·50
Explanation
Finding the selling price for a 25% profit
A person buys 100 pens at a net cost of Rs 600 (after a 10% discount), incurs 15% selling expenses on this net cost, and wants a 25% profit.
| Step | Calculation |
|---|---|
| Net cost price | Rs 600 (given) |
| Selling expenses | 15% of 600 = Rs 90 |
| Total cost (cost + expenses) | 600 + 90 = Rs 690 |
| Required selling price (25% profit on total cost) | 690 × 1.25 = Rs 862.50 |
Why we add selling expenses before applying profit:
| Point | Detail |
|---|---|
| Total cost basis | Net cost + selling expenses = the true cost incurred |
| Profit margin | Applied to this combined total cost, not the net cost alone |
Answer: (c) Rs 862.50.
Why each option is right or wrong
- (a) Incorrect. Rs 802.50 applies the profit margin to the wrong base amount.
- (b) Incorrect. Rs 811.25 also doesn't match the correct total-cost-based calculation.
- (c) CORRECT. (600 + 90) × 1.25 = Rs 862.50, the correct selling price for a 25% profit on total cost.
- (d) Incorrect. Rs 875 overstates the required selling price.
Key point
Total cost = net cost (Rs 600) + selling expenses (15% of 600 = Rs 90) = Rs 690. Applying a 25% profit margin: 690 × 1.25 = Rs 862.50.
Remember
Net cost Rs 600 + 15% selling expenses (Rs 90) = Rs 690 total cost; 25% profit gives a selling price of Rs 862.50.
Common mistakes
- Applying the 25% profit margin to the net cost alone, forgetting to first add the selling expenses.
- Miscalculating the 15% selling expense amount.
- Confusing 'profit on cost' with 'profit on selling price', which would require a different formula.
Exam tip
For profit-margin problems with added expenses: Total cost = base cost + expenses, THEN apply the profit percentage to this combined total.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Profit and Loss)
- NCERT Class VIII Mathematics — Comparing Quantities