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.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.
(a)1/4
(b)1/3
(c)3/4
(d)1/5
2.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
3.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.
(a)£3244.80
(b)£3120.00
(c)£244.80
(d)£3240.00
4.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.
(a)£65
(b)£67.50
(c)£60
(d)£70
5.A laptop costs £800 when new. Its value decreases by 25% of its value at the start of each year. Work out how much value the laptop loses in the second year.
(a)£150
(b)£450
(c)£350
(d)£200
6.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
7.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
8.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
9.A sponsored walk raised £350 for charity. 20% of the money raised is spent on equipment. Work out how much is spent on equipment.
(a)£35
(b)£280
(c)£70
(d)£17.50
10.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.
(a)90%
(b)80%
(c)20%
(d)125%
11.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
12.The population of a village is 1200. It is predicted to grow by 5% next year. Work out the predicted population after 1 year, to the nearest whole number.
(a)1260
(b)1800
(c)1205
(d)60
13.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%
14.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.
(a)£600.00
(b)£408.00
(c)£624.32
(d)£5624.32
15.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
16.40% of a number is 12 more than 25% of the same number. Work out the number.
(a)48
(b)80
(c)15
(d)30
17.Work out 35% of 180.
(a)45
(b)63
(c)145
(d)126
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.Work out 15% of £40, using 10% and 5%.
(a)£6
(b)£4
(c)£600
(d)£2
20.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
21.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
22.Work out 1/2 of 1/4 of 80.
(a)20
(b)10
(c)60
(d)40

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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