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Reverse percentages

Free Printable Reverse percentages PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free reverse percentages worksheets (PDF), GCSE maths past paper questions and worked solutions for Reverse percentages (5C). This is a Grade 5 number topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from IGCSE MT, Maths Genie, Corbett Maths, Maths Made Easy, Dr Frost, Naiker Maths, Dr Austin, 1st Class Maths, Dr Frost (B. Blocks), Maths4EveryOne, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our reverse percentages revision notes and worked examples with diagrams, try real GCSE past paper reverse percentages questions with step-by-step solutions, or download a PDF of all reverse percentages worksheet links.

Free Reverse percentages PDF Worksheets & Answers

Grade 5 • Topic 5C
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IGCSE (9–1) past paper booklet
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Edexcel exam questions & solutions
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AQA exam questions & solutions
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Building Blocks skill sheet & answers
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GCSE 9–1 practice booklet & solutions
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
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PMT (IGCSE)
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GCSE Maths Grade 5 Revision Notes & Method

Guide to Reverse percentages: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Reverse percentage questions give you the new value after a percentage change and ask for the original amount (100%). Never work out the percentage of the new amount—the percentage was calculated from the original amount, not the final one.

First write the new percentage by adding to 100% (for an increase) or subtracting from 100% (for a decrease/sale). Then either divide the new amount by the decimal multiplier, or divide to find 1% and multiply by 100 to get 100%.

Example 1: In a 15% off sale, a jacket costs £68. Work out the normal price of the jacket before the sale.

Solution:

Sale price is 100% − 15% = 85% of the original price
85% = £68 (decimal multiplier = 0.85)
1% = £68 ÷ 85 = £0.80
100% = £0.80 × 100 (or £68 ÷ 0.85) = £80
Answer: £80

Example 2: After a 6% pay rise, Maya earns £25,440 per year. What was her salary before the pay rise?

Solution:

New salary is 100% + 6% = 106% of original salary
Decimal multiplier = 1.06
Original × 1.06 = £25,440
Original = £25,440 ÷ 1.06 = £24,000
Answer: £24,000
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Reverse percentages Questions & Answers

Past Paper Example 1 AQA Nov 2021 3H Q14 3 marks
Phil sells ties.
He increases the original price of each tie by 10% to £13.20
A month later he announces a sale: 10% OFF ALL TIES.
SALE10% OFFALL TIES
Phil says,
“The ties will be back to their original price, because each change was by 10%”
Is he correct?
Tick a box: [ ] Yes [ ] No
Show working to support your answer.
Worked Solution & Mark Scheme (3 marks)
Original price = £13.20 ÷ 1.10 = £12.00 M1
Sale price = £13.20 × 0.90 = £11.88 M1
Since £11.88 ≠ £12.00, Phil is incorrect (tick No). A1
Answer: No, sale price is £11.88 whereas original price was £12.00
Past Paper Example 2 IGCSE Jan 2022 1HR Q10 / 1FR Q24 6 marks
Jonty has a storage container in the shape of a cuboid, as shown in the diagram.
3 m2.5 m12 mDiagram NOTaccurately drawn
Jonty is going to paint the outside of his storage container, apart from the base which is shown shaded in the diagram.
He needs enough paint to cover the four sides and the top.
Each tin of paint covers an area of 15 m2
The cost of each tin of paint recently increased by 10%
After the increase, the cost of each tin of paint is £26.95
Jonty says
"Before the increase, I could have bought enough paint for less than £200"
Show that Jonty is correct.
Show your working clearly.
Worked Solution & Mark Scheme (6 marks)
Area = 15 + 72 + 30 = 117 m² M2
Tins = 117 ÷ 15 = 7.8 → 8 tins M2
Original price per tin = £26.95 ÷ 1.1 = £24.50 M1
Cost for 8 tins = 8 × £24.50 = £196 < £200. C1
Answer: £196 < £200 (Jonty is correct)
Past Paper Example 3 IGCSE Nov 2024 1F Q24 / 1H Q7 4 marks
Shop A and Shop B have offers for buying the same type of laptop.
Shop AOur normal price£475Get 16% off ournormal priceShop BGet 15% off ournormal priceOnly pay £408
The normal price of the laptop in Shop A is different to the normal price of the laptop in Shop B
Which shop gives more money off their normal price?
Show your working clearly.
Worked Solution & Mark Scheme (4 marks)
Shop A discount = 0.16 × £475 = £76 M1
Shop B normal price = £408 ÷ 0.85 = £480 M1
Shop B discount = £480 − £408 = £72 M1
Therefore Shop A gives more money off. A1
Answer: Shop A (£76 off vs £72 off in Shop B)

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