Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Reverse percentages

Finding the original amount.

17 original questions, 50 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

In a sale, all prices are reduced by 15%.

The sale price of a jumper is £68.

Work out the normal price of the jumper.

2 marks
Show answer
£80
2

The price of a rail ticket increased by 20%.

The ticket now costs £54.

Work out the price of the ticket before the increase.

2 marks
Show answer
£45
3

The price of a jacket is reduced by 10%.

The reduced price is £63.

Work out the price of the jacket before the reduction.

2 marks
Show answer
£70
4

The price of a printer, including VAT at 20%, is £90.

Work out the price of the printer before VAT was added.

2 marks
Show answer
£75
5

The population of a town increased by 12% between 2015 and 2025.

The population in 2025 was 26 880.

Work out the population in 2015.

2 marks
Show answer
24000
6

In a sale there is 30% off all prices.

Kofi pays £59.36 for a coat in the sale.

Work out the price of the coat before the sale.

2 marks
Show answer
£84.80
7

Sunita’s salary was increased by 4%.

Her new salary is £31 200 a year.

Work out her salary before the increase.

3 marks
Show answer
£30 000
8

Dana gets a 5% pay rise.

Her new rate of pay is £13.65 per hour.

Work out her rate of pay before the rise.

2 marks
Show answer
£13
9

In 2024 the population of a town decreased by 8% to 46 000.

  1. Work out the population of the town before the decrease.
  2. In 2025 the population increased by 3%. Work out the population of the town after this increase.
4 marks
Show answer
a) 50 000 b) 47 380
10

The value of a car depreciates by 20% each year.

At the end of 2 years the car is worth £10 368.

Work out the value of the car 2 years ago.

3 marks
Show answer
£16200
11

Aisha puts £1500 into a savings account for one year.

At the end of the year the interest is taxed at 20%. After tax is taken off, Aisha receives £36 interest.

Work out the annual interest rate of the account before tax.

4 marks
Show answer
3%
12

The value of a house increased by 8% in 2024 and then by 5% in 2025.

At the end of 2025 the house was worth £226 800.

Work out the value of the house at the start of 2024.

3 marks
Show answer
£200000
13

A delivery van lost 12% of its value in the first year and then 25% of its remaining value in the second year.

After two years the van is worth £5940.

Work out the value of the van when it was new.

3 marks
Show answer
£9000
14

The price of a television was reduced by 20% in a sale.

In a final clearance, the sale price was reduced by a further 10%.

The clearance price is £216.

  1. Work out the original price of the television.
  2. Show that the two reductions together are equivalent to a single reduction of 28%.
4 marks
Show answer
a) £300 b) 0.8 x 0.9 = 0.72, so the final price is 72% of the original, a 28% reduction
15

In a sale, the price of a coat is reduced by 27 of its original price.

The sale price of the coat is £45

Work out the original price of the coat.

3 marks
Show answer
£63
16

VAT at 20% is added to the price of a laptop.

The shop then takes 10% off the price including VAT.

Sam pays £648 for the laptop.

Work out the price of the laptop before VAT was added.

4 marks
Show answer
£600
17

Ines put a sum of money into a savings account for 3 years.

The account paid 4% compound interest in the first year, then 2.5% compound interest in each of the next 2 years.

At the end of the 3 years the account held £8741.20.

  1. Work out the sum of money Ines put into the account.
  2. Work out the total interest she earned.
5 marks
Show answer
a) £8000 b) £741.20

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

All Grade 5 topics