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GCSE · Number - Percentages

5.3D Reverse Percentages: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

State the decimal multiplier equivalent to an increase of 8%.

(Total for Question 1 is 1 mark)

State the decimal multiplier equivalent to a decrease of 35%.

(Total for Question 2 is 1 mark)

A price is increased by 12%. State the single decimal multiplier used to find the new price directly from the original price.

(Total for Question 3 is 1 mark)

State the single decimal multiplier equivalent to a decrease of 6%.

(Total for Question 4 is 1 mark)

The price of a train ticket increased by 10%. The new price is £71.50. Work out the original price of the ticket.

(Total for Question 5 is 2 marks)

A number is increased by 20% to give 96. Find the original number.

(Total for Question 6 is 2 marks)

After a 15% decrease, a quantity of paint is 68 litres. Find the original quantity of paint.

(Total for Question 7 is 2 marks)

A price is reduced by 25% in a sale to £54. Work out the original price.

(Total for Question 8 is 2 marks)

A number is increased by 4% to give 130. Find the original number.

(Total for Question 9 is 2 marks)

A quantity is decreased by 8% to give 138. Find the original quantity.

(Total for Question 10 is 2 marks)

The price of a laptop after a 12% increase is £280. Work out the original price of the laptop.

(Total for Question 11 is 3 marks)

After a pay rise of 3%, Kwame's monthly salary is £2,729.50. Work out his monthly salary before the rise.

(Total for Question 12 is 3 marks)

A shop reduces the price of a jacket by 30% in a sale. The sale price is £42. Work out the original price of the jacket.

(Total for Question 13 is 3 marks)

The number of pupils at a school increased by 6% this year to 477. Work out the number of pupils at the school last year.

(Total for Question 14 is 3 marks)

A car service costs £96, including VAT at 20%. Work out the cost of the service before VAT was added.

(Total for Question 15 is 3 marks)

A motorbike's value decreased by 15% during its first year of ownership. After the decrease, the motorbike is worth £10,200. Rhys says, 'The motorbike must have been worth more than £12,000 when it was new.' Determine, showing your working, whether Rhys is correct.

(Total for Question 16 is 4 marks)

A company's profit increased by 10% in 2024, and then increased by a further 5% in 2025. The profit in 2025 was £46,200. Work out the company's profit in 2023, before either increase.

(Total for Question 17 is 4 marks)

A tumble dryer is on sale with a 20% discount already applied to its original price. VAT at 20% is then added to the discounted price, giving a final price of £372. A shop advert claims the tumble dryer was originally priced at £450 before any discount.

(a)Work out the original price of the tumble dryer, before the discount was applied.(3)

(b)State, with a reason, whether the shop's advert is correct.(2)

(Total for Question 18 is 5 marks)

A shop increases the price of a coffee machine by 30%, then reduces this new price by 30% in a clearance sale. The final sale price is £109.20. Work out the original price of the coffee machine, and state whether the final sale price is greater than, less than, or equal to the original price.

(Total for Question 19 is 4 marks)

Two market stalls sell the same style of scarf. At Stall A, the original price was increased by 25% to a sale-day price of £30. At Stall B, the original price was decreased by 20% to a sale-day price of £30.

(a)Work out the original price of the scarf at Stall A.(2)

(b)Work out the original price of the scarf at Stall B.(2)

(c)State which stall's scarf had the greater original price, giving a reason.(1)

(Total for Question 20 is 5 marks)

A company's revenue increased by 8% in Year 1, and then decreased by 5% in Year 2. The Year 2 revenue was £513,000. Work out the revenue before Year 1, and work out the overall percentage change in revenue from before Year 1 to the end of Year 2.

(Total for Question 21 is 6 marks)

Nia is asked to find the original price of a jumper that was reduced by 15% in a sale to £68. She writes: 'Original price = 68 / 1.15 = 59.13 (2 d.p.)' Explain the error in Nia's method, and work out the correct original price of the jumper.

(Total for Question 22 is 6 marks)

A furniture shop has a sale. The price of a sofa is reduced by 20%. The price of an armchair is reduced by 30%. Before the sale, the armchair's original price was 3/4 of the sofa's original price. After the reductions, the sofa costs £55 more than the armchair. Work out the original price of the sofa.

(Total for Question 23 is 7 marks)

Mark scheme · 5.3D Reverse Percentages: Fluency and Exam Drill

Question 1

B1 1.08 oe
Answer: 1.08

Question 2

B1 0.65 oe
Answer: 0.65

Question 3

B1 1.12 oe
Answer: 1.12

Question 4

B1 0.94 oe
Answer: 0.94

Question 5

M1 correct multiplier 1.10 oe, or 71.50 / 1.1 seen
A1 £65 cao
Answer: £65

Question 6

M1 correct multiplier 1.20 oe, or 96 / 1.2 seen
A1 80 cao
Answer: 80

Question 7

M1 correct multiplier 0.85 oe, or 68 / 0.85 seen
A1 80 litres cao
Answer: 80 litres

Question 8

M1 correct multiplier 0.75 oe, or 54 / 0.75 seen
A1 £72 cao
Answer: £72

Question 9

M1 correct multiplier 1.04 oe, or 130 / 1.04 seen
A1 125 cao
Answer: 125

Question 10

M1 correct multiplier 0.92 oe, or 138 / 0.92 seen
A1 150 cao
Answer: 150

Question 11

M1 correct multiplier 1.12 oe
M1 complete method 280 / 1.12
A1 £250 cao
Answer: £250

Question 12

M1 correct multiplier 1.03 oe
M1 complete method 2729.50 / 1.03
A1 £2,650 cao
Answer: £2,650

Question 13

M1 correct multiplier 0.70 oe
M1 complete method 42 / 0.70
A1 £60 cao
Answer: £60

Question 14

M1 correct multiplier 1.06 oe
M1 complete method 477 / 1.06
A1 450 pupils cao
Answer: 450 pupils

Question 15

M1 correct multiplier 1.20 oe
M1 complete method 96 / 1.2
A1 £80 cao
Answer: £80

Question 16

M1 correct multiplier 0.85 oe
M1 complete method 10200 / 0.85
A1 £12,000 cao
B1 ft correct conclusion, e.g. Rhys is not correct because the motorbike was worth exactly £12,000, not more than £12,000
Answer: £12,000; Rhys is not correct (the motorbike was worth exactly £12,000).

Question 17

M1 46200 / 1.05 (or an equivalent first step to undo the 2025 increase)
A1 £44,000 (interim 2024 profit)
M1 44000 / 1.1 (or an equivalent step to undo the 2024 increase)
A1 £40,000 cao
Answer: £40,000

Question 18

(a) M1 combined multiplier 0.8 x 1.2 = 0.96 oe, or an equivalent stepwise method (e.g. 372 / 1.2 = 310 seen)
(a) M1 complete method to find the original price, e.g. 372 / 0.96, or 310 / 0.8
(a) A1 £387.50 cao
(a) Answer: £387.50
(b) B1 ft correct decision that the advert is not correct, referencing the £387.50 found in part (a)
(b) B1 correct supporting figure, e.g. states the original price was £62.50 less than the advertised £450 (450 - 387.50 = 62.50)
(b) Answer: No; the original price was £387.50, which is £62.50 less than the advertised £450.

Question 19

M1 combined multiplier 1.3 x 0.7 = 0.91 oe (or an equivalent stepwise method)
M1 complete method 109.20 / 0.91
A1 £120 cao
B1 ft states less than, since the combined multiplier 0.91 is less than 1
Answer: £120; the final sale price is less than the original price.

Question 20

(a) M1 correct multiplier 1.25 oe, or 30 / 1.25 seen
(a) A1 £24 cao
(a) Answer: £24
(b) M1 correct multiplier 0.8 oe, or 30 / 0.8 seen
(b) A1 £37.50 cao
(b) Answer: £37.50
(c) B1 ft Stall B, since £37.50 is greater than £24
(c) Answer: Stall B, since £37.50 > £24.

Question 21

M1 combined multiplier 1.08 x 0.95 = 1.026 oe (or an equivalent stepwise method)
M1 complete method 513000 / 1.026
A1 £500,000 cao
M1 identifies that the overall multiplier 1.026 corresponds to a percentage change
A1 2.6% cao
B1 ft states an increase (not a decrease), since 1.026 is greater than 1
Answer: £500,000; an overall increase of 2.6%.

Question 22

B1 identifies the error, e.g. Nia has divided by 1.15 (the multiplier for a 15% increase), but the price was decreased by 15%, so she should divide by 0.85, not 1.15
M1 correct multiplier for a 15% decrease, 0.85 oe
M1 complete method 68 / 0.85
A1 £80 cao
B1 valid check, e.g. 80 x 0.85 = 68
B1 correct concluding statement that the original price is £80, not the £59.13 Nia found
Answer: £80 (Nia's £59.13 is incorrect).

Question 23

M1 expresses the armchair's original price in terms of the sofa's, e.g. armchair original = (3/4)S oe, where S is the sofa's original price
M1 correct multiplier for the sofa, 0.8 oe
M1 correct expression for the armchair's sale price, 0.7 x (3/4)S oe = 0.525S oe
M1 forms a correct equation, e.g. 0.8S - 0.525S = 55 oe
M1 simplifies to 0.275S = 55 oe
A1 S = 200, i.e. £200 cao
B1 ft valid check, e.g. sofa original £200 gives sale price £160; armchair original £150 gives sale price £105; difference 160 - 105 = £55, matches
Answer: £200

Reverse Percentages: Fluency and Exam Drill - Worksheets, Questions and Revision