Percentage change Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Percentage change questions. See exactly how to solve problems on percentage multiplier, percentage increase, percentage decrease, money.

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

Worked solution

  1. Start from the original amount as 100%

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

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

  2. Add the percentage change

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

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

  3. Write that percentage as a decimal

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

    Dividing by 100 turns the percentage into the multiplier 1.2. Multiplying by 1.21.2 carries out the 20% increase in one go.

Answer
1.21.2
Question 2
1 markeasy
Write down the multiplier for a 15% decrease.

Worked solution

  1. Start from the original amount as 100%

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

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

  2. Subtract the percentage change

    100%−15%=85%100\% - 15\% = 85\%

    A 15% decrease leaves you with 85% of the original amount.

  3. Write that percentage as a decimal

    85%=85%÷100%=0.8585\% = 85\% \div 100\% = 0.85

    Dividing by 100 turns the percentage into the multiplier 0.85. Multiplying by 0.850.85 carries out the 15% decrease in one go.

Answer
0.850.85
Question 3
1 markeasy
Write down the multiplier for a 5% increase.

Worked solution

  1. Start from the original amount as 100%

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

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

  2. Add the percentage change

    100%+5%=105%100\% + 5\% = 105\%

    A 5% increase leaves you with 105% of the original amount.

  3. Write that percentage as a decimal

    105%=105%÷100%=1.05105\% = 105\% \div 100\% = 1.05

    Dividing by 100 turns the percentage into the multiplier 1.05. Multiplying by 1.051.05 carries out the 5% increase in one go.

Answer
1.051.05
Question 4
1 markeasy
Write down the multiplier for a 30% decrease.

Worked solution

  1. Start from the original amount as 100%

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

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

  2. Subtract the percentage change

    100%−30%=70%100\% - 30\% = 70\%

    A 30% decrease leaves you with 70% of the original amount.

  3. Write that percentage as a decimal

    70%=70%÷100%=0.770\% = 70\% \div 100\% = 0.7

    Dividing by 100 turns the percentage into the multiplier 0.7. Multiplying by 0.70.7 carries out the 30% decrease in one go.

Answer
0.70.7
Question 5
1 markeasy
Write down the multiplier for an 8% increase.

Worked solution

  1. Start from the original amount as 100%

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

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

  2. Add the percentage change

    100%+8%=108%100\% + 8\% = 108\%

    A 8% increase leaves you with 108% of the original amount.

  3. Write that percentage as a decimal

    108%=108%÷100%=1.08108\% = 108\% \div 100\% = 1.08

    Dividing by 100 turns the percentage into the multiplier 1.08. Multiplying by 1.081.08 carries out the 8% increase in one go.

Answer
1.081.08

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