# Profit and Loss Questions with Answers, Formulas and Tricks

> Profit and loss formulas, marked price and discount shortcuts, and solved questions with step-by-step explanations for campus placement aptitude tests.

Source: https://www.sansal.in/aptitude/profit-and-loss · Last updated: 2026-09-19 · How often it appears: Very high. Typically 2-4 questions in a service-company aptitude paper.

Profit and loss is percentages applied to trade. Almost every question reduces to picking the right base — cost price or marked price — and the candidates who lose marks here usually lost them by computing a percentage against the wrong one.

## Concepts

### Profit percentage is always on cost price

Unless a question explicitly says otherwise, profit % and loss % are calculated on the cost price. Discount %, by contrast, is always calculated on the marked price. Mixing these two bases is the single most common error in this topic.

### The marked price chain

A typical question layers three numbers: cost price (what the seller paid), marked price (the sticker), and selling price (what was actually charged after discount). Work in that order and express each as a multiple of CP — set CP = 100 and the algebra disappears.

### Equal selling prices always lose

If two items sell for the same price, one at x% profit and the other at x% loss, the net result is always a loss of (x²/100)%. It is never break-even. This is a favourite question because the intuitive answer — zero — is wrong.

## Formulas

| Formula | Rule | Note |
| --- | --- | --- |
| Profit | Profit = SP − CP |  |
| Profit % | Profit % = ((SP − CP) / CP) × 100 |  |
| Selling price from profit % | SP = CP × (100 + p) / 100 |  |
| Cost price from selling price | CP = (SP × 100) / (100 + p) |  |
| Discount | Discount % = ((MP − SP) / MP) × 100 | On marked price — not on cost price. |
| Same SP, x% profit and x% loss | Net loss % = x² / 100 | Always a loss, never break-even. |

## Worked examples

### Example 1

**Question:** An article bought for ₹400 is sold for ₹500. Find the profit percentage.

**Solution:**

1. Profit = SP − CP = 500 − 400 = 100
2. Profit % = (Profit / CP) × 100 = (100 / 400) × 100

**Answer:** 25% profit

### Example 2

**Question:** A shopkeeper marks goods 25% above cost price and then allows a 10% discount. What is the net profit percentage?

**Solution:**

1. Set CP = 100 so the percentages become rupees.
2. Marked price = 100 × 1.25 = 125
3. Selling price after 10% discount = 125 × 0.90 = 112.5
4. Profit = 112.5 − 100 = 12.5 on a cost of 100

**Answer:** 12.5% profit

**Check:** Note it is not 25 − 10 = 15%. The discount is taken on 125, not on 100.

### Example 3

**Question:** Two articles are each sold for ₹1,200. One is sold at 20% profit and the other at 20% loss. What is the overall result?

**Solution:**

1. Find each cost price separately — this is where the loss hides.
2. CP of the profitable one = 1200 / 1.20 = ₹1,000
3. CP of the loss-making one = 1200 / 0.80 = ₹1,500
4. Total CP = 1000 + 1500 = ₹2,500. Total SP = 2 × 1200 = ₹2,400
5. Loss = 2500 − 2400 = ₹100 on ₹2,500

**Answer:** An overall loss of ₹100, which is 4%

**Check:** The shortcut gives the same thing: x²/100 = 400/100 = 4% loss.

## Practice questions

1. An item costing ₹250 is sold for ₹300. The profit percentage is:
   - A. 15%
   - B. 20%
   - C. 25%
   - D. 30%
   - **Answer:** B. 20% — Profit = 50. (50 / 250) × 100 = 20%.

2. A article costs ₹600 and is sold at 20% profit. The selling price is:
   - A. ₹680
   - B. ₹700
   - C. ₹720
   - D. ₹750
   - **Answer:** C. ₹720 — SP = 600 × 1.20 = ₹720.

3. An article sold for ₹480 at a 20% loss. Its cost price was:
   - A. ₹540
   - B. ₹576
   - C. ₹600
   - D. ₹620
   - **Answer:** C. ₹600 — CP = 480 / 0.80 = ₹600. Dividing, not multiplying — the loss applies to CP.

4. An item marked at ₹800 is sold after a 15% discount. The selling price is:
   - A. ₹660
   - B. ₹680
   - C. ₹700
   - D. ₹720
   - **Answer:** B. ₹680 — 800 × 0.85 = ₹680.

5. Two items sell at the same price, one at 10% profit and one at 10% loss. The net result is:
   - A. No profit no loss
   - B. 1% loss
   - C. 2% loss
   - D. 1% profit
   - **Answer:** B. 1% loss — x²/100 = 100/100 = 1% loss. Equal selling prices always produce a loss.

6. If the cost price of 100 articles equals the selling price of 80 articles, the profit percentage is:
   - A. 20%
   - B. 25%
   - C. 30%
   - D. 33.3%
   - **Answer:** B. 25% — Let each SP = 1, so SP of 80 = 80 = CP of 100. CP each = 0.8. Profit = 0.2 on 0.8 → 25%.

7. A trader marks goods 40% above cost and gives a 25% discount. The profit percentage is:
   - A. 5%
   - B. 10%
   - C. 15%
   - D. 20%
   - **Answer:** A. 5% — CP = 100 → MP = 140 → SP = 140 × 0.75 = 105. Profit = 5%.

8. A "buy 3 get 1 free" offer is equivalent to a discount of:
   - A. 20%
   - B. 25%
   - C. 30%
   - D. 33.3%
   - **Answer:** B. 25% — You pay for 3 and receive 4. Discount = 1/4 = 25% on the marked value of 4 items.

## Where marks get lost

- Computing discount on cost price instead of marked price.
- Subtracting the markup and discount percentages directly (25% up then 10% off is not 15% profit).
- Assuming equal selling prices at equal profit and loss percentages break even.
- Multiplying instead of dividing when going from selling price back to cost price.

## Related topics

- [Percentages](https://www.sansal.in/aptitude/percentages)
- [Ratio & Proportion](https://www.sansal.in/aptitude/ratio-and-proportion)
- [Averages](https://www.sansal.in/aptitude/averages)

Practise these on Sansal: https://www.sansal.in/practice/aptitude