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Reverse Percentages - Worksheets, Questions and Revision

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GCSE · Number - Percentages

5.3 Reverse Percentages

EDEXCEL 1MA1 · Calculator allowed · about 70 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Revision notes: Reverse Percentages

Reverse percentages (finding the original amount) work backwards from a value AFTER a percentage increase or decrease to find the value BEFORE the change. The given amount represents a percentage that is not 100%, so you divide, not multiply, to undo the change.

  1. Work out what percentage the given (final) amount represents of the original: 100% plus the increase, or 100% minus the decrease.
  2. Convert that percentage to a decimal multiplier (divide by 100).
  3. Divide the given amount by this multiplier to find the original 100% amount. Do NOT find a percentage of the given amount; that is a common error.
  4. Check your answer: applying the original percentage change to your answer should give back the amount you started with.
Worked example. After a 20% pay rise, Priya's salary is 30000 pounds. Work out her salary before the rise.
  1. A 20% rise means the new salary is 100% + 20% = 120% of the original.
  2. 120% as a decimal multiplier is 1.2.
  3. Original salary = 30000 / 1.2 = 25000 pounds.
  4. Check: 25000 x 1.2 = 30000, which matches the given amount.
Answer: 25000 pounds.
1
A number is increased by 10% to give 99. Work out the original number.
(Total for Question 1 is 2 marks)
2
In a sale, all prices are reduced by 25%. The sale price of a jumper is £18. Work out the original price of the jumper before the sale.
(Total for Question 2 is 2 marks)
3
A washing machine costs £342 including VAT at 20%. Work out the cost of the washing machine before VAT was added.
(Total for Question 3 is 2 marks)
4
A shop reduces the price of a coat by 30% in a sale. The sale price of the coat is £84.
Which calculation gives the original price of the coat?
  • A) 84 x 0.30
  • B) 84 / 0.70
  • C) 84 x 1.30
  • D) 84 x 0.70
(Total for Question 4 is 1 mark)
5
A number is decreased by 40% to give 54.
Which calculation gives the original number?
  • A) 54 / 0.60
  • B) 54 x 0.60
  • C) 54 / 1.40
  • D) 54 x 1.40
(Total for Question 5 is 1 mark)
6
The number of members of a gym increased by 12% this year. There are now 504 members. Work out the number of members last year.
(Total for Question 6 is 2 marks)
7
A jacket is reduced by 30% in a sale. The sale price of the jacket is £56.
A student's working to find the original price is shown below.

56 x 1.3 = 72.80

The student concludes that the original price of the jacket was £72.80.
(a)Identify the error in the student's method.(1)
(b)Work out the correct original price of the jacket.(2)
(Total for Question 7 is 3 marks)
8
Tom says, 'A laptop's price was reduced by 15% in a sale. To find the original price from the sale price, you should increase the sale price by 15%.'
Tom is wrong.
Explain why Tom is wrong. You should include an example with numbers to support your answer.
(Total for Question 8 is 2 marks)
9
Priya's monthly salary was increased by 4%. Her new monthly salary is £2,496. Work out Priya's monthly salary before the increase.
(Total for Question 9 is 2 marks)
10
A car was bought new. In its first year, the value of the car decreased by 18%. At the end of the first year, the car was worth £10,824.
(a)Work out the value of the car when it was new.(2)
(b)In the car's second year, its value is expected to decrease by a further 15% (from its value at the end of the first year). Work out the expected value of the car at the end of the second year. Give your answer to the nearest penny.(2)
(Total for Question 10 is 4 marks)
11
A restaurant automatically adds a service charge of 12.5% to the price of a meal. The total bill, including the service charge, is £81.00. Work out the price of the meal before the service charge was added.
(Total for Question 11 is 2 marks)
12
The population of a village decreased by 8% between 2015 and 2025. In 2025 the population was 4,600. Work out the population of the village in 2015.
(Total for Question 12 is 2 marks)
13
The price of a house increased by 5% over the last year. The house is now worth £294,000. Work out the price of the house one year ago.
(Total for Question 13 is 2 marks)
14
A shop increases the price of a laptop by 20%. In a later sale, the shop reduces this new price by 20%. The final sale price of the laptop is £249.60.
Work out the price of the laptop before the first increase.
(Total for Question 14 is 3 marks)
15
A trader buys a bicycle and later sells it, making a loss of 20% on the price she paid. She sells the bicycle for £276.
Work out how much the trader paid for the bicycle.
(Total for Question 15 is 2 marks)
16
For each part, work out the original number before the stated percentage change was made.
(a)A number is increased by 6% to give 4,770. Work out the original number.(2)
(b)A number is decreased by 35% to give 260. Work out the original number.(2)
(c)A number is increased by 2.5% to give 861. Work out the original number.(2)
(Total for Question 16 is 6 marks)
17
In 2024, 68% of the students at a school passed a mathematics examination. This pass rate of 68% was 25% higher than the pass rate in 2023.
Work out the percentage of students who passed the mathematics examination in 2023.
(Total for Question 17 is 2 marks)
18
Chloe buys a sofa on a deferred payment plan.
She pays a deposit equal to 15% of the cash price of the sofa. The remaining amount is then increased by 8%, to cover a credit charge, before being split into equal monthly instalments.
The remaining amount, after the 8% credit charge has been added, is £642.60.
Work out the cash price of the sofa.
(Total for Question 18 is 3 marks)
19
A retailer buys bicycles from a wholesaler. The retailer adds a mark-up of 20% to the wholesale price to get the normal shop price. In a sale, the shop price is then reduced by 15%.
The final sale price of a bicycle is £142.80.
Work out the price the retailer paid the wholesaler for the bicycle.
(Total for Question 19 is 3 marks)
20
The price of a train ticket increases by 4% every year.
This year, after the increase, the ticket costs £108.16. This price already includes an increase of 4% that was applied last year, and a separate increase of 4% that was applied the year before that.
Work out the price of the train ticket two years ago, before either of these two increases.
(Total for Question 20 is 3 marks)
21
A number n is increased by 15%. The result is then decreased by 20%. The final value is 3 less than n.
(a)Show that this information can be written as 0.92n = n - 3(2)
(b)Work out the value of n.(2)
(Total for Question 21 is 4 marks)
Mark scheme · 5.3 Reverse Percentages

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

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Question 1

2 marks

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Question 3

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Question 4

1 mark
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1 mark
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Question 6

2 marks

Question 7

3 marks
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Question 8

2 marks
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Question 9

2 marks

Question 10

4 marks
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Question 11

2 marks

Question 12

2 marks

Question 13

2 marks

Question 14

3 marks

Question 15

2 marks

Question 16

6 marks
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Question 17

2 marks

Question 18

3 marks

Question 19

3 marks

Question 20

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Question 21

4 marks
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