Percentage Change –

Percentage change questions are among the most common on GCSE Maths exams. Instead of being given a percentage and asked to apply it, you are given two values and must calculate what percentage one has changed relative to the other. This skill is essential for topics ranging from profit and loss to population growth.

What Is Percentage Change?

Percentage change measures how much a quantity has increased or decreased relative to its original value, expressed as a percentage. If a price rises from £40 to £50, the percentage change tells you by what percentage the price went up.

The direction of the change matters. A percentage increase means the new value is larger than the original. A percentage decrease means the new value is smaller. The formula is the same in both cases — the sign of the answer tells you the direction.

It is crucial that you always divide by the original value, not the new value. This is one of the most common errors students make in exams.

Key Formulas

Step-by-Step Method

1. Write down the original value and the new value.
2. Calculate the change: new value − original value.
3. Divide the change by the original value.
4. Multiply by 100 to convert to a percentage.
5. State whether the change is an increase or a decrease.

Worked Example 1 — Foundation Level

Question: A shirt was priced at £40. In a sale, the price is reduced to £34. Find the percentage decrease.

Working:

Step 1 — Original value = £40, new value = £34.

Step 2 — Change = 34 − 40 = −6 (a decrease of £6).

Step 3 — Percentage change = (6 / 40) × 100 = 15%.

Answer: 15% decrease

Worked Example 2 — Higher Level

Question: The population of a town increased from 24,500 to 28,175. Calculate the percentage increase. Give your answer to 1 decimal place.

Working:

Step 1 — Original value = 24,500, new value = 28,175.

Step 2 — Change = 28,175 − 24,500 = 3,675.

Step 3 — Percentage change = (3,675 / 24,500) × 100 = 15.0%.

Answer: 15.0% increase

Worked Example 3 — Exam Style

Question: A shop buys a coat for £35 and sells it for £56. Work out the percentage profit. (3 marks)

Working:

Step 1 — Cost price (original) = £35, selling price (new) = £56.

Step 2 — Profit = 56 − 35 = £21.

Step 3 — Percentage profit = (21 / 35) × 100 = 60%.

Answer: 60% profit

Common Mistakes

• Dividing by the new value instead of the original. The formula requires you to divide by the original. In the shirt example, dividing £6 by £34 gives the wrong answer.
• Forgetting to multiply by 100. The division gives a decimal (e.g. 0.15). You must multiply by 100 to express it as a percentage.
• Confusing percentage change with the actual change. The actual change is in the same units as the values (e.g. £6). The percentage change is a relative measure (e.g. 15%).

Exam Tips

• Always identify which value is the original. In profit/loss questions, the original is the cost price. In growth questions, the original is the starting value.
• Write the formula first, then substitute. This earns you a method mark on AQA, Edexcel, and OCR papers.
• If the question asks for an answer to a specific number of decimal places, do not round early — only round your final answer.

Practice Questions

Q1 (Foundation): A games console was £300. Its price rises to £345. Find the percentage increase.

Q2 (Foundation): A car depreciates from £12,000 to £9,600. Find the percentage decrease.

Q3 (Higher): Last year 480 students passed an exam. This year 552 passed. Work out the percentage increase to 1 decimal place.

Practise percentage change questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Percentages
• Reverse Percentages
• Percentage of an Amount

Summary

• Percentage change = (change ÷ original) × 100.
• Always divide by the original value, never the new value.
• A positive result means an increase; a negative result means a decrease.
• Write the formula and substitute clearly to earn method marks.
• This skill applies to profit/loss, depreciation, population changes, and many other contexts.