22 questions on percentage change, reverse percentages, simple and compound interest, and depreciation.
💷 Percentages and compound interest
Percentages appear on all three papers and in more contexts than any other single topic — prices, wages, interest, VAT, population, depreciation. This sheet covers the whole of it in order. It begins with percentage of an amount and percentage change, including finding the percentage rather than applying it; moves to multipliers, which make everything after this easier; then to reverse percentages, where you are given the value after the change and asked for the original, and where subtracting instead of dividing is the commonest error in the topic; then to simple interest, compound interest and depreciation, where the multiplier is raised to a power rather than multiplied by the number of years. The last few questions mix the types without labelling them, because on the paper they are not labelled either.
- 1.40% of a number is 12 more than 25% of the same number. Work out the number.
- 2.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.
- 3.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.
- 4.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.
- 5.A concert hall has 300 seats. 20% of the seats are in the balcony. Work out how many of the seats are in the balcony.
- 6.A population of penguins on an island is 2400. The population is predicted to grow by 7% each year. Work out the predicted population after 2 years, to the nearest whole number.
- 7.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.
- 8.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.
- 9.Work out 25% of 200.
- 10.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.
- 11.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.
- 12.Before a charity campaign, donations were £6400 per month. Donations grew by 8% in the first year after the campaign, and then fell by 3% in the second year as interest faded. Work out the amount donated per month at the end of the second year, to the nearest pound.
- 13.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.
- 14.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.
- 15.Work out 15% of £40, using 10% and 5%.
- 16.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.
- 17.A sponsored walk raised £350 for charity. 20% of the money raised is spent on equipment. Work out how much is spent on equipment.
- 18.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
- 19.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.
- 20.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.
- 21.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
- 22.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
What is on this worksheet?
The sheet holds 22 questions drawn from the MathsUK bank — the content areas covered: Ratio, proportion and rates of change, Number (statements R9, R16, N12). It is pitched at GCSE Foundation and takes about 40 minutes to work through in full. It is built for independent practice, with full answers at the end for self-marking.
How to use the sheet well
- Print it or open it on screen — both work. Printing is A4; the screen view fits phones and tablets.
- Do all 22 questions before checking — about 40 minutes is the guide, but there is no time pressure.
- Check the answers — press “Show answers” or print the answer page separately.
- Redo the questions you got wrong — twice as effective as doing 22 fresh ones.
- “New questions” — builds a fresh sheet on the same statements, so you can practise again without repeats.
Why this sheet helps
MathsUK worksheets use questions graded by difficulty and a fair spread of correct-answer positions (the answer is not always (a)) — so the student really has to think about each question rather than guess a pattern. Every question is tagged to a DfE content statement and checked before it enters the bank. The answers come with a step-by-step explanation, not just a value — so a wrong answer becomes a lesson.
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