Percentage Change
Get to grips with percentage change using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on calculating percentage increase and decrease, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Percentage change = (change ÷ original) × 100 — always divide by the original.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Percentage change measures how much a quantity has risen or fallen relative to where it started. The formula is the change divided by the original amount, multiplied by \(100\).
The word original is the whole difficulty. The denominator is always the starting value, never the new one, and never the difference. Using the wrong denominator produces an answer that is plausible but wrong.
The same formula covers profit and loss, percentage increase and decrease, and percentage error. A positive result is an increase and a negative result a decrease, though questions usually ask you to state which rather than rely on the sign.
Revision notes
The formula
Percentage change \(= \dfrac{\text{change}}{\text{original}} \times 100\).
If a price rises from \(£40\) to \(£50\), the change is \(£10\) and the original is \(£40\), so the increase is \(\frac{10}{40} \times 100 = 25\%\).
Profit and loss
Profit is selling price minus cost price, and percentage profit uses the cost price as the denominator.
Buying at \(£80\) and selling at \(£100\) gives a profit of \(£20\), so the percentage profit is \(\frac{20}{80} \times 100 = 25\%\). Dividing by the selling price would give 20 percent, which is wrong.
Increase and decrease are not symmetric
A 20 percent rise followed by a 20 percent fall does not return you to the start, because the second percentage applies to a larger amount.
\(£100\) rising 20 percent gives \(£120\); falling 20 percent from there gives \(£96\), not \(£100\).
Key points
- Percentage change \(= \dfrac{\text{change}}{\text{original}} \times 100\).
- The denominator is always the original amount.
- Percentage profit uses the cost price.
- State whether the change is an increase or a decrease.
- A rise then an equal fall does not return to the start.
- Round to a sensible accuracy, usually 1 decimal place.
Worked examples
Example 1
A price rises from \(£80\) to \(£92\). Find the percentage increase.
Working
Example 2
An item bought for \(£250\) is sold for \(£200\). Find the percentage loss.
Working
Example 3
A population falls from \(4500\) to \(4140\). Find the percentage decrease.
Working
Common mistakes
Dividing by the new amount.
The denominator is always the original value, or the answer is systematically wrong.
Dividing by the change itself.
The change is the numerator, not the denominator.
Assuming a rise then an equal fall cancels out.
£100 up 20% then down 20% gives £96, because the second percentage acts on a larger amount.
Not saying whether it is an increase or decrease.
The question usually requires this in words, not just a number.
Exam tips
- Write down the original amount before calculating anything.
- For profit and loss, the denominator is the cost price.
- Always state increase, decrease, profit or loss in your answer.
- Sense-check: a change smaller than the original gives under 100 percent.
Key terms
- Percentage change
- The change expressed as a percentage of the original amount.
- Original amount
- The starting value, used as the denominator.
- Profit
- The amount by which the selling price exceeds the cost price.
- Cost price
- The amount paid for an item.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.