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.A company's profit this year is 130% of last year's profit. Last year's profit was £40,000. Work out this year's profit.
- 2.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.
- 3.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.
- 4.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
- 5.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
- 6.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.
- 7.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.
- 8.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.
- 9.Work out 35% of 180.
- 10.A quiz has 50 questions. Freya answers 10% of them incorrectly. Work out how many questions she answers incorrectly.
- 11.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
- 12.A machine is bought for £8500. Its value depreciates by 6% each year. Work out the value of the machine after 3 years, to the nearest pound.
- 13.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.
- 14.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.
- 15.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
- 16.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.
- 17.A pack contains 20 stickers. Noah gives 1/5 of the pack to his sister. Work out how many stickers he gives away.
- 18.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
- 19.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
- 20.Work out 1/2 of 1/4 of 80.
- 21.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.
- 22.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.
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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