Sheet № 229 · Foundation + Higher · AQA · Edexcel · OCR
Percentage Profit and Loss –
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. The
§Key definitions
Profit
occurs when the selling price is greater than the cost price. Loss occurs when the selling price is less than the cost price.
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%.
Question:
A shopkeeper buys a phone for £120 and sells it for £150. Calculate the percentage profit.
Answer:
The percentage profit is 25%.
Q1 (Foundation):
A jacket is bought for £40 and sold for £52. What is the percentage profit?
§Formulas to memorise
Profit = Selling Price - Cost Price
Loss = Cost Price - Selling Price
Percentage Profit = (Profit / Cost Price) x 100
Percentage Loss = (Loss / Cost Price) x 100
Profit: occurs when the selling price is greater than the cost price. Loss occurs when the selling price is less than the cost price.
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%.
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. — 4. Multiply by 100 to convert to a percentage.
State whether it is a profit or a loss — in your answer.
Worked example
A shopkeeper buys a phone for £120 and sells it for £150. Calculate the percentage profit.
Working:
⚠ 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.