22 questions on percentage change, reverse percentages, simple and compound interest, and depreciation.

💷 Percentages and compound interest

Maths · GCSE Foundation · 22 questions · ~40 min

MathsUKwww.geekhero.co.uk

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.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.
(a)18
(b)4
(c)24
(d)36
2.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.
(a)54
(b)126
(c)150
(d)30
3.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.
(a)£27.00
(b)£15.00
(c)£9.00
(d)£33.00
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.
(a)£598
(b)£494
(c)£478.40
(d)£416
5.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.
(a)3
(b)30
(c)25
(d)24
6.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.
(a)55
(b)75
(c)20
(d)60
7.After a price increase of 10%, a laptop costs £330. Work out the original price.
(a)£3,300
(b)£300
(c)£363
(d)£297
8.A pack contains 20 stickers. Noah gives 1/5 of the pack to his sister. Work out how many stickers he gives away.
(a)4
(b)5
(c)100
(d)16
9.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.
(a)£6912
(b)£7104
(c)£6720
(d)£6705
10.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.
(a)£12,000
(b)£52,000
(c)£5,200
(d)£40,130
11.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%
12.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.
(a)£48
(b)£72
(c)£75
(d)£12
13.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.
(a)£7560.00
(b)£10497.60
(c)£7617.60
(d)£8280.00
14.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.
(a)12%
(b)4%
(c)112%
(d)0.04%
15.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
16.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
17.Work out 25% of 200.
(a)50
(b)100
(c)25
(d)800
18.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.
(a)£18
(b)£8
(c)£138
(d)£12
19.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.
(a)2978
(b)3156
(c)2809
(d)2950
20.Work out 50% of 60.
(a)6
(b)3000
(c)120
(d)30
21.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.
(a)200 g
(b)128 g
(c)240 g
(d)40 g
22.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.
(a)£72
(b)£640
(c)£80
(d)£6480

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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