GCSE Percentage change Practice Questions

Free GCSE Percentage change practice questions with full step-by-step worked solutions. Covers percentage multiplier, percentage increase, percentage decrease, money. Practise exam-style problems and check your method.

percentage multiplierpercentage increasepercentage decreasemoneypercentage changechange over original
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Write down the multiplier for a 20%20\% increase.
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Worked solution

  1. Start from the original amount as 100%100\%

    original=100%\text{original} = 100\%

    Every amount is 100%100\% of itself before anything happens to it.

  2. Add the percentage change

    100%+20%=120%100\% + 20\% = 120\%

    A 20%20\% increase leaves you with 120%120\% of the original amount.

  3. Write that percentage as a decimal

    120%=120%÷100%=1.2120\% = 120\% \div 100\% = 1.2

    Dividing by 100100 turns the percentage into the multiplier 1.21.2. Multiplying by 1.21.2 carries out the 20%20\% increase in one go.

Answer
1.21.2
Question 2
1 markeasy
When you work out a percentage change, what do you divide the change by?
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Worked solution

  1. Recall the percentage change formula

    percentage change=changeoriginal×100\text{percentage change} = \frac{\text{change}}{\text{original}} \times 100

    The change is compared with the amount you started with.

  2. See why the original is the right base

    £40→£44:  440×100=10%\pounds 40 \to \pounds 44: \; \frac{4}{40} \times 100 = 10\%

    A £4\pounds 4 rise on £40\pounds 40 is a 10%10\% increase, because the £4\pounds 4 is judged against the £40\pounds 40 you started with.

  3. See what goes wrong with the new amount

    444×100=9.09...%≠10%\frac{4}{44} \times 100 = 9.09...\% \ne 10\%

    Dividing by the new amount, £44\pounds 44, gives 9.09%9.09\% — the wrong answer. The original is always the base.

Answer
the original amount\text{the original amount}
Question 3
2 marksintermediate
A tree is 3.5 m3.5\,\mathrm{m} tall. Over one year it grows to 4.2 m4.2\,\mathrm{m}. Work out the percentage increase in its height.
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Worked solution

  1. Identify the original amount and the new amount

    original=3.5,new=4.2\text{original} = 3.5, \quad \text{new} = 4.2

    The starting value is 3.53.5 and it finishes at 4.24.2.

  2. Work out the size of the change

    4.2−3.5=0.74.2 - 3.5 = 0.7

    The amount has gone up by 0.70.7.

  3. Write down the percentage change formula

    percentage change=changeoriginal×100\text{percentage change} = \frac{\text{change}}{\text{original}} \times 100

    The change is always divided by the ORIGINAL amount, not the new one.

  4. Substitute the numbers

    0.73.5×100\frac{0.7}{3.5} \times 100

    The change 0.70.7 is divided by the original 3.53.5.

  5. Work out the division, then multiply by 100100

    0.73.5=0.2,0.2×100=20\frac{0.7}{3.5} = 0.2, \quad 0.2 \times 100 = 20

    As a decimal the change is 0.20.2 of the original, which is 20%20\%.

  6. State the percentage change

    20% increase20\% \text{ increase}

    Check with a multiplier: 4.2÷3.5=1.24.2 \div 3.5 = 1.2, and a multiplier of 1.21.2 is exactly a 20%20\% increase. ✓

Answer
20% increase20\% \text{ increase}
Question 4
4 markshard
A charity raised £4500\pounds 4500 in 20232023 and £5850\pounds 5850 in 20242024. In 20252025 the amount raised was 20%20\% less than in 20242024. Work out the percentage change from 20232023 to 20252025.
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Worked solution

  1. Write down the amount raised in 20232023

    2023:  £45002023: \; \pounds 4500

    The question asks for the change from 20232023 to 20252025, so £4500\pounds 4500 is the original amount.

  2. Work out the rise from 20232023 to 20242024

    £5850−£4500=£1350\pounds 5850 - \pounds 4500 = \pounds 1350

    Donations rose by £1350\pounds 1350 in the first year.

  3. Express the 20242024 rise as a percentage

    13504500×100=30%\frac{1350}{4500} \times 100 = 30\%

    A 30%30\% rise from 20232023 to 20242024.

  4. Find the multiplier for the 20252025 fall

    100%−20%=80%=0.8100\% - 20\% = 80\% = 0.8

    In 20252025 the charity raised 20%20\% less than in 20242024, so multiply the 20242024 figure by 0.80.8.

  5. Work out the amount raised in 20252025

    £5850×0.8=£4680\pounds 5850 \times 0.8 = \pounds 4680

    The 20%20\% fall acts on the £5850\pounds 5850 raised in 20242024, not on the £4500\pounds 4500 raised in 20232023. The 20252025 total is £4680\pounds 4680.

  6. Compare 20252025 with 20232023

    £4680>£4500\pounds 4680 > \pounds 4500

    Even after the fall, 20252025 is still ahead of 20232023 — so the overall change is an increase.

  7. Work out the size of the overall change

    £4680−£4500=£180\pounds 4680 - \pounds 4500 = \pounds 180

    Over the two years the charity raised £180\pounds 180 more.

  8. Divide by the ORIGINAL 20232023 amount

    1804500=0.04\frac{180}{4500} = 0.04

    The £180\pounds 180 is compared with the £4500\pounds 4500 the charity started from in 20232023.

  9. Turn it into a percentage

    0.04×100=4%0.04 \times 100 = 4\%

    The overall change from 20232023 to 20252025 is a 4%4\% increase.

  10. Check with multipliers

    1.3×0.8=1.041.3 \times 0.8 = 1.04

    A 30%30\% rise then a 20%20\% fall gives a single multiplier of 1.041.04, a 4%4\% increase. ✓ Note that +30%+30\% then −20%-20\% is NOT +10%+10\%.

Answer
4% increase4\% \text{ increase}
Question 5
6 markschallenging
A hotel room costs £80\pounds 80 per night. In August the price rises by 40%40\%. In October the August price falls by 30%30\%. In January the October price falls by a further 25%25\%. Work out the overall percentage change from the original £80\pounds 80.
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Worked solution

  1. Write down the original price

    original=£80\text{original} = \pounds 80

    The overall percentage change is measured against this £80\pounds 80.

  2. August: find the multiplier

    100%+40%=140%=1.4100\% + 40\% = 140\% = 1.4

    A 40%40\% rise means multiplying by 1.41.4.

  3. August: work out the price

    £80×1.4=£112\pounds 80 \times 1.4 = \pounds 112

    The August price is £112\pounds 112.

  4. October: find the multiplier

    100%−30%=70%=0.7100\% - 30\% = 70\% = 0.7

    A 30%30\% fall means multiplying by 0.70.7.

  5. October: apply it to the AUGUST price

    £112×0.7=£78.40\pounds 112 \times 0.7 = \pounds 78.40

    The 30%30\% comes off £112\pounds 112 (that is £33.60\pounds 33.60), not off the original £80\pounds 80. The October price is £78.40\pounds 78.40.

  6. January: find the multiplier

    100%−25%=75%=0.75100\% - 25\% = 75\% = 0.75

    A further 25%25\% fall means multiplying by 0.750.75.

  7. January: apply it to the OCTOBER price

    £78.40×0.75=£58.80\pounds 78.40 \times 0.75 = \pounds 58.80

    The January price is £58.80\pounds 58.80.

  8. Multiply the three multipliers together

    1.4×0.7×0.751.4 \times 0.7 \times 0.75

    Successive percentage changes combine by multiplying their multipliers, never by adding the percentages.

  9. Work out the product in stages

    1.4×0.7=0.98,0.98×0.75=0.7351.4 \times 0.7 = 0.98, \quad 0.98 \times 0.75 = 0.735

    The single equivalent multiplier is 0.7350.735.

  10. Check the single multiplier against the price

    £80×0.735=£58.80\pounds 80 \times 0.735 = \pounds 58.80

    The single multiplier gives the same January price. ✓

  11. Compare the multiplier with 11

    0.735<10.735 < 1

    The multiplier is below 11, so the room is cheaper in January than it was originally.

  12. Turn the multiplier into a percentage change

    (0.735−1)×100=−26.5(0.735 - 1) \times 100 = -26.5

    The overall change is a 26.5%26.5\% decrease.

  13. Confirm from the prices

    80−58.8080×100=21.2080×100=26.5%\frac{80 - 58.80}{80} \times 100 = \frac{21.20}{80} \times 100 = 26.5\%

    The price has fallen by £21.20\pounds 21.20, and £21.20\pounds 21.20 out of the original £80\pounds 80 is 26.5%26.5\%. ✓

  14. Watch the common error

    +40%−30%−25%=−15%≠−26.5%+40\% - 30\% - 25\% = -15\% \ne -26.5\%

    Adding the percentages gives a 15%15\% fall, which is badly wrong. Notice too that +40%+40\% then −30%-30\% is not +10%+10\%: 1.4×0.7=0.981.4 \times 0.7 = 0.98, already a 2%2\% fall.

  15. State the overall percentage change

    26.5% decrease26.5\% \text{ decrease}

    The January price is 26.5%26.5\% below the original £80\pounds 80.

Answer
26.5% decrease26.5\% \text{ decrease}

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