Work backwards from a price after a percentage change to the original 100%, by dividing by the multiplier. It is on Foundation and Higher, aimed at grade 5. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Reverse percentages undo a change. If a price is £48 after a 20% increase, £48 is 120% of the original, so original =48÷1.20. If £48 is after a 20% decrease, it is 80% of the original, so ÷0.80. The trap is treating £48 as 100% and adding or subtracting 20% of it.
Write the multiplier, then divide. A 'was £… before VAT' or 'sale price £…, original?' question is this every time. Check: the original after an increase should be smaller than the new price; after a decrease it should be larger.
The given amount is the result after the change, not the original. Divide by the multiplier: after 25% off, divide by 0.75; after a 10% rise, divide by 1.1. Never add 25% back on — that is the classic reverse-percentage trap.
Objectives
Find an original price after a percentage decrease.
Find an original price after a percentage increase.
Write a multiplier, and find a percentage change between two amounts.
Key points
Recognise a reverse percentage question: the amount given is the new amount, and you want the original.
Write the multiplier for an increase (1+100p) or a decrease (1−100p).
Divide the new amount by the multiplier to get the original.
Use the build-up method without a calculator: find what 1% or 5% is worth, then scale to 100%.
Worked examples
Example 1
After a 20% decrease the price is £80. Work out the original price.
2 marks
Identify remaining percentage: 100% - 20% = 80%, so multiplier is 0.8.
Divide the sale price by 0.8: 80 / 0.8 = 100.
The original price was £100.
Answer: 100
Common slips
Slip: Subtract 20% of 80. The percentage was deducted from the original, not from 80.
Slip: James calculated 80 - 16 = 64. You must divide by the multiplier to undo the percentage decrease.
Slip: Conclude £64. 80 divided by 0.8 is 100.
Example 2
After a 10% increase the price is £66. Work out the original price.
2 marks
Identify new percentage: 100% + 10% = 110%, so multiplier is 1.1.
Divide the increased price by 1.1: 66 / 1.1 = 60.
The original price was £60.
Answer: 60
Common slips
Slip: Subtract 10% of 66. You cannot undo a percentage increase by subtracting that percentage from the new price.
Slip: Kelly calculated 66 - 6.6 = 59.40. Dividing by 1.1 correctly returns to the starting value.
Slip: Conclude £59.40. 66 divided by 1.1 is 60.
Example 3
A price falls from £100 to £80. Work out the percentage decrease.
3 marks
Calculate the decrease amount: 100 - 80 = 20.
Express the drop as a percentage of original: (20 / 100) × 100% = 20%.
The decrease is 20%.
Answer: 20
Common slips
Slip: Take 80 as the percentage change. 80 is the final value, not the difference.
Slip: Lucas wrote 80. Percentage change compares the difference to the original amount.
Slip: Conclude 80%. A drop of 20 from 100 is 20%.
Questions and answers
GCSE Maths reverse percentages questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
After a 25% decrease the price is £60. Work out the original price.
Show answer
Answer: 80
Remaining is 75%, multiplier is 0.75.
Divide: 60 / 0.75 = 80.
M1 — Remaining is 75%, multiplier is 0.75.
A1 — Divide: 60 / 0.75 = 80.
Question 2 Easy2 marks
After a 10% decrease the price is £54. Work out the original price.
Show answer
Answer: 60
Remaining is 90%, multiplier is 0.9.
Divide: 54 / 0.9 = 60.
M1 — Remaining is 90%, multiplier is 0.9.
A1 — Divide: 54 / 0.9 = 60.
Question 3 Medium2 marks
After a 20% increase the price is £72. Work out the original price.
Show answer
Answer: 60
New amount is 120%, multiplier is 1.2.
Divide: 72 / 1.2 = 60.
M1 — New amount is 120%, multiplier is 1.2.
A1 — Divide: 72 / 1.2 = 60.
Question 4 Medium2 marks
After a 25% increase the price is £50. Work out the original price.
Show answer
Answer: 40
New amount is 125%, multiplier is 1.25.
Divide: 50 / 1.25 = 40.
M1 — New amount is 125%, multiplier is 1.25.
A1 — Divide: 50 / 1.25 = 40.
Question 5 Hard2 marks
Write down the multiplier for a 20% decrease.
Show answer
Answer: 0.8
Calculate 100% - 20% = 80%.
Convert to decimal: 80% = 0.8.
M1 — Calculate 100% - 20% = 80%.
A1 — Convert to decimal: 80% = 0.8.
Question 6 Hard2 marks
Write down the multiplier for a 10% increase.
Show answer
Answer: 1.1
Calculate 100% + 10% = 110%.
Convert to decimal: 110% = 1.1.
M1 — Calculate 100% + 10% = 110%.
A1 — Convert to decimal: 110% = 1.1.
Question 7 Exam-style3 marks
After a 30% decrease the price is £42. Work out the original price.
Show answer
Answer: 60
Remaining percentage is 100% - 30% = 70%, so multiplier is 0.7.
Divide by multiplier: 42 / 0.7 = 60.
M1 — 100% - 30% = 70%, or multiplier 0.7
M1 — 42 ÷ 0.7, or 42 ÷ 70 × 100
A1 — £60
Common mistakes
Most lost marks on this topic are one slip.
Subtracting the percent from the new price
Divide by the multiplier
Using 0.1 as the multiplier for a 10% increase
A 10% increase multiplies by 1.1
Writing the new amount as the percentage change
Compare the drop with the original
Spot the slip
After a 20% decrease the price is £80. Will adds 20% to £80 and says £96. What was the original price?
100
96
60
Show the slip
100 80 is 80% of the original: 80 ÷ 0.8 = 100.
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 as a decimal on its own line — that line usually earns the method mark.
Finish with a forwards check; it takes ten seconds and protects the accuracy mark.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.