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Profit and loss explained: cost price, selling price and percentages
Cost price, selling price, profit, loss and percentage profit explained with worked examples in rupees, the four formulas to remember and the mistakes students make.
Profit and loss questions look like word problems, but they use one idea: compare what a shopkeeper paid with what the shopkeeper got. Once the two prices are clear, the rest is percentages.
The words you need
- Cost price (CP): what the seller paid to buy or make the article.
- Selling price (SP): what the customer pays.
- Profit: when SP is more than CP. Profit = SP − CP.
- Loss: when SP is less than CP. Loss = CP − SP.
The four formulas
| To find | Formula |
|---|---|
| Profit percent | Profit ÷ CP × 100 |
| Loss percent | Loss ÷ CP × 100 |
| SP after a profit of p% | CP × (100 + p) ÷ 100 |
| SP after a loss of p% | CP × (100 − p) ÷ 100 |
To go backwards, from SP to CP after a profit of p%, use CP = SP × 100 ÷ (100 + p). The key point: profit and loss percentages are always taken on the cost price, not on the selling price.
Worked examples
1. Finding profit percent. An article costs ₹200 and is sold for ₹250. Profit = 250 − 200 = ₹50. Profit percent = 50 ÷ 200 × 100 = 25%.
2. Finding loss percent. An article costs ₹400 and is sold for ₹320. Loss = 400 − 320 = ₹80. Loss percent = 80 ÷ 400 × 100 = 20%.
3. Finding the selling price. A shopkeeper buys an article for ₹800 and sells it at a 15% profit. SP = 800 × 115 ÷ 100 = ₹920.
4. Finding the cost price. An article is sold for ₹1,150 at a 15% profit. CP = 1,150 × 100 ÷ 115 = ₹1,000.
5. A bundle. A shopkeeper buys 12 pens for ₹120 and sells them at ₹12 each. CP = ₹120 and SP = 12 × 12 = ₹144. Profit = ₹24, so profit percent = 24 ÷ 120 × 100 = 20%.
Mistakes to avoid
- Dividing by the selling price. For 25% profit on ₹200, the profit is 25% of ₹200 (₹50), not 25% of the selling price.
- Adding the percent to the wrong number. To increase ₹800 by 15%, multiply by 1.15. Do not add 15 to 800.
- Mixing up profit and selling price. The profit is the difference. The selling price already contains the cost.
- Forgetting the units. Write ₹ or % in the answer, so it is clear whether you found an amount or a percentage.
Check your answer
A profit percent or a loss percent is always a positive number, and the word you choose shows the direction. If the selling price is higher than the cost price, the word must be profit. A quick check is to start from the answer: ₹200 plus 25% of ₹200 is ₹250, which matches example 1.
Practise it
- Profit and loss practice online: eight questions at a time with instant feedback.
- Profit and loss worksheets with an answer key, made fresh each time.
- Percent Power: a game that practises finding percentages.
- Percentages explained simply if percentages themselves feel shaky.
Common questions
What is the difference between profit and profit percent?
Profit is an amount of money (for example ₹50). Profit percent compares that amount with the cost price (₹50 out of ₹200 is 25%).
How do I find the cost price if I know the selling price and the profit percent?
Divide the selling price by (100 + profit percent) and multiply by 100. For ₹1,150 at 15% profit: 1,150 ÷ 115 × 100 = ₹1,000.
Is profit percent calculated on cost price or selling price?
On the cost price, in school maths. Some businesses talk about a margin on the selling price, which is a different number, so always check which one a question means.
Is discount the same as loss?
No. A discount is a reduction from the marked price. A seller can still make a profit after a discount if the selling price is above the cost price.
This guide is general information. For exams, follow your school, teacher and official exam board, and use your own judgement about what suits your child.