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 box holds 140 pens. 25% of the pens are red. Work out how many of the pens are red.
(a)35
(b)105
(c)25
(d)70
2.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%
3.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.
(a)£2200.00
(b)£2205.00
(c)£205.00
(d)£2100.00
4.A charity fun run raises money through entry fees and donations. Entry fees raise £1,260, which is 60% of the total amount raised. Work out how much money was raised through donations.
(a)£504
(b)£1,890
(c)£840
(d)£2,100
5.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
6.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.
(a)140 students
(b)300 students
(c)200 students
(d)260 students
7.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
8.A savings account pays 3.5% compound interest each year. Bilal invests £1200. Work out how much interest, in total, he earns after 2 years, to the nearest penny.
(a)£85.47
(b)£1285.47
(c)£84.00
(d)£42.00
9.Write 3/4 as a percentage.
(a)133%
(b)34%
(c)0.75%
(d)75%
10.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
11.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.
(a)£177.60
(b)£444.00
(c)£88.80
(d)£266.40
12.Work out 10% of 30% of £200.
(a)£60
(b)£80
(c)£20
(d)£6
13.After a price increase of 10%, a laptop costs £330. Work out the original price.
(a)£3,300
(b)£300
(c)£363
(d)£297
14.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%
15.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
16.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
17.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
18.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
19.Work out 50% of 60.
(a)6
(b)3000
(c)120
(d)30
20.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
21.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
22.Work out 8% of £250.
(a)£25
(b)£2
(c)£200
(d)£20

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.

Similar worksheets worth a look

✏️ Paper 1 non-calculator warm-up — Foundation · 20 questions · ~25 min
🎯 Grade 4 pass booster · 25 questions · ~40 min
⚖️ Foundation to Higher crossover check · 20 questions · ~35 min
⚗️ Ratio and proportion mastery — Higher · 24 questions · ~45 min