Increase or decrease an amount by a percentage, and work out the percentage change between two values. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Percentage change compares the difference with the original, not with the new value. percentage change=originaldifference×100. A price that goes from £40 to £46 is a 406×100=15% increase. Using £46 on the bottom is the classic wrong method.
A multiplier is often cleaner: new =original×(1±r). Profit and loss, population change and simple interest at this grade are all this one idea. Simple interest is not compound — you find one year's interest and multiply by the number of years.
Increase and decrease with a multiplier (1.12 or 0.88) so you do not forget to add or subtract at the end. Percentage change is originaldifference×100. The original is always the starting value, even when the question gives the new price first.
Objectives
Increase by 20% means multiply by 1.2.
The question may ask for the increase itself, or for the price after the increase.
Change ÷ original × 100 gives the percentage change.
Key points
Write a multiplier for a percentage increase or decrease.
Increase or decrease an amount with the multiplier, or by finding the percentage and adding/subtracting.
Work out percentage change using originalchange×100.
Handle two changes one after the other by multiplying the multipliers.
Worked examples
Example 1
Increase 30 by 10%.
2 marks
The multiplier for a 10% increase is 1 + 10/100 = 1.1.
30 × 1.1 = 33.
The new amount is 33.
Answer: 33
Common slips
Slip: The multiplier for a 12% increase is 1 + 10/100 = 1.1. That changes a number from the question, so it answers a different question.
Slip: 30 + 1.1 = 31.1. That uses addition, but this step needs multiplication.
Slip: The new amount is 37. That does not match the working above it.
Example 2
Decrease 50 by 10%.
2 marks
The multiplier for a 10% decrease is 1 − 10/100 = 0.9.
50 × 0.9 = 45.
The new amount is 45.
Answer: 45
Common slips
Slip: The multiplier for a 12% decrease is 1 − 10/100 = 0.9. That changes a number from the question, so it answers a different question.
Slip: 50 + 0.9 = 50.9. That uses addition, but this step needs multiplication.
Slip: The new amount is 49. That does not match the working above it.
Example 3
A price rises from £40 to £46. Work out the percentage increase.
Slip: The change is 48 − 40 = 6. That changes a number from the question, so it answers a different question.
Slip: Percentage change = change ÷ original × 103 = 6 ÷ 40 × 100 = 15. That changes a number in the working, so the step no longer follows from the one before.
Slip: The percentage increase is 19%. That does not match the working above it.
Questions and answers
GCSE Maths percentage change questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A price of £60 increases by 15%. What is the new price?
Show answer
Answer: 69
The multiplier is 1.15.
£60 × 1.15.
M1 — The multiplier is 1.15.
A1 — Answer 69
Question 2 Easy2 marks
A price of £90 decreases by 10%. What is the new price?
Show answer
Answer: 81
The multiplier is 0.9.
£90 × 0.9.
M1 — The multiplier is 0.9.
A1 — Answer 81
Question 3 Medium2 marks
After a 20% increase a fare is £90. What was the fare before the increase?
Show answer
Answer: 75
Divide by 1.2.
£90 ÷ 1.2.
M1 — Divide by 1.2.
A1 — Answer 75
Question 4 Medium2 marks
After a 10% decrease a fare is £54. What was the fare before the decrease?
Show answer
Answer: 60
Divide by 0.9.
£54 ÷ 0.9.
M1 — Divide by 0.9.
A1 — Answer 60
Question 5 Hard2 marks
£400 grows by 10% a year for 3 years. What is the final amount?
Show answer
Answer: 532.4
Multiply by 11/10 three times.
Start from £400.
M1 — Multiply by 11/10 three times.
A1 — Answer 532.4
Question 6 Hard2 marks
A laptop worth £200 depreciates by 20% a year for 2 years. What is it worth then?
Show answer
Answer: 128
Each year multiplies by 4/5.
Do that twice from £200.
M1 — Each year multiplies by 4/5.
A1 — Answer 128
Question 7 Exam-style3 marks
£500 grows by 10% a year for 3 years. What is the final amount?
Show answer
Answer: 665.5
Multiply by 11/10 three times.
Start from £500.
M1 — Multiply by 11/10 three times.
M1 — Start from £500.
A1 — Answer 665.5
Common mistakes
Most lost marks on this topic are one slip.
Adding the percent on as a raw number.
20% of £40 is £8, not 20.
Using 1.2 for a decrease.
A 20% decrease multiplies by 0.8.
Dividing the change by the final amount.
Percentage change divides by the original.
Spot the slip
A 10% increase uses the multiplier
1.1
0.1
10
Show the slip
1.1 You keep the original 100% and add 10%.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the multiplier down before you use it — it earns a method mark even if you press the wrong button.
Money answers to 2 decimal places: £76.80, not £76.8.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.