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.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%
2.Work out 2/5 of 45.
(a)36
(b)27
(c)18
(d)9
3.Write 3/4 as a percentage.
(a)133%
(b)34%
(c)0.75%
(d)75%
4.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.
(a)21%
(b)81%
(c)20%
(d)19%
5.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.
(a)£675.31
(b)£72
(c)£672
(d)£618
6.Work out 50% of 60.
(a)6
(b)3000
(c)120
(d)30
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.
(a)200 m
(b)1050 m
(c)150 m
(d)50 m
8.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
9.The value of a rare coin increases by 12% each year. The coin is currently worth £270. Work out the value of the coin after 2 years, giving your answer to the nearest penny.
(a)£334.80
(b)£338.68
(c)£338.69
(d)£302.40
10.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
(a)£1,000
(b)£600
(c)£825
(d)£200
11.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.
(a)£11.00
(b)£66.60
(c)£1.60
(d)£5.40
12.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%
13.2/3 of an amount of money is £30. Work out the amount.
(a)£15
(b)£45
(c)£20
(d)£90
14.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
15.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.
(a)£6970
(b)£7511
(c)£7990
(d)£7060
16.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
17.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
(a)60
(b)460
(c)340
(d)415
18.A quiz has 50 questions. Freya answers 10% of them incorrectly. Work out how many questions she answers incorrectly.
(a)5
(b)10
(c)500
(d)45
19.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
20.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
(a)75%
(b)133%
(c)25%
(d)18%
21.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
22.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8

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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