Profit, loss and discount

Objective. Solve contextual percentage problems and justify decisions.

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2. Worked example
3. Practice
4. Feedback
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Learn: the key idea

Profit, loss and discount problems apply percentage calculations to buying and selling contexts, where you compare a cost price with a selling price. Profit occurs when the selling price is higher than the cost price, and the percentage profit is the profit divided by the cost price, multiplied by 100. A discount reduces a marked price by a percentage before the item is sold. To decide whether a deal is worthwhile, calculate the actual amounts involved and compare them directly rather than just comparing percentages, since the same percentage can mean different amounts on different prices.

Worked example

A shop buys a lamp for £40 and sells it for £52. Calculate the percentage profit made on the lamp.

1 $Find the profit: £52 - £40 = £12$
2 $Write profit over cost price: 12/40$
3 $Convert to a percentage: (12 \div 40) \times 100$
4 $Calculate the result: 30%$

Answer: 30%

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Common mistake. Pupils often calculate percentage profit using the selling price as the denominator instead of the cost price, so a £20 profit on a £80 cost item is wrongly divided by £100 instead of £80, giving 20% instead of the correct 25%.

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