Percentage profit and loss is a practical topic that appears frequently in GCSE Maths exams, particularly in the context of business, shopping and investment scenarios. You need to be able to calculate profit or loss as a percentage of the cost price, work out the selling price given a desired profit margin, and understand break-even. These questions test your percentage skills in a real-world setting and are examined at both Foundation and Higher tier. This guide provides clear methods and worked examples.
What Is Percentage Profit and Loss?
Profit occurs when the selling price is greater than the cost price. Loss occurs when the selling price is less than the cost price.
Key Formulas
The percentage is always calculated as a fraction of the cost price (what you originally paid), not the selling price.
Break-even
Break-even is the point where selling price equals cost price — there is no profit and no loss. Percentage profit at break-even is 0%.
Step-by-Step Method
- Identify the cost price (CP) and the selling price (SP) from the question.
- Calculate the profit or loss: Profit = SP - CP (if positive, it is profit; if negative, it is a loss).
- Divide the profit or loss by the cost price.
- Multiply by 100 to convert to a percentage.
- State whether it is a profit or a loss in your answer.
Worked Example 1 — Foundation Level
Question: A shopkeeper buys a phone for £120 and sells it for £150. Calculate the percentage profit.
Working:
Profit = 150 - 120 = £30
Percentage profit = (30 / 120) x 100 = 25%
Answer: The percentage profit is 25%.
Worked Example 2 — Higher Level
Question: A car is bought for £8,000 and sold two years later for £5,600. Calculate the percentage loss.
Working:
Loss = 8000 - 5600 = £2,400
Percentage loss = (2400 / 8000) x 100 = 30%
Answer: The car was sold at a 30% loss.
Worked Example 3 — Exam Style
Question: A trader wants to make a 40% profit on an item that cost £65. What should the selling price be?
Working:
Step 1: 40% of £65 = 0.40 x 65 = £26
Step 2: Selling price = Cost price + Profit = 65 + 26 = £91
Alternatively, use the multiplier: Selling price = 65 x 1.40 = £91
Answer: The trader should sell the item for £91.
Common Mistakes
- Dividing by the selling price instead of the cost price. Percentage profit and loss are always calculated relative to the cost price (the original amount). Dividing by the selling price gives the wrong answer.
- Confusing profit with percentage profit. A profit of £30 is not the same as 30% profit. You must divide by the cost price and multiply by 100.
- Forgetting to state profit or loss. The question may ask you to identify which one applies. Always state clearly whether the result is a profit or a loss.
- Using the wrong multiplier. For a 40% profit, multiply by 1.40 (not 0.40). For a 15% loss, multiply by 0.85.
Exam Tips
- Write out the formula before substituting values — this earns a method mark on its own.
- If a question asks "what selling price gives a 20% profit," use the multiplier approach: SP = CP x 1.20. This is quicker and less error-prone.
- In multi-step problems (buy, repair, sell), make sure you include all costs in the total cost price before calculating profit.
- Always read whether the question asks for the profit amount or the percentage profit — they are different things.
Practice Questions
Q1 (Foundation): A jacket is bought for £40 and sold for £52. What is the percentage profit?
Q2 (Foundation): A tablet is bought for £200 and sold for £170. What is the percentage loss?
Q3 (Higher): A trader buys 50 mugs at £2 each and sells them at £3.50 each. 8 mugs are broken and cannot be sold. Calculate the overall percentage profit.
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Summary
- Profit = Selling Price - Cost Price. Loss = Cost Price - Selling Price.
- Percentage profit or loss is always calculated as a fraction of the cost price, multiplied by 100.
- To find a selling price for a given profit %, use the multiplier: SP = CP x (1 + profit/100).
- For a loss, the multiplier is SP = CP x (1 - loss/100).
- Break-even means the selling price equals the cost price (0% profit or loss).
- Include all costs (purchase, repair, delivery) when calculating total cost price.
- Always state whether your answer is a profit or a loss.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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