Percentage Change (Edexcel GCSE Maths: Foundation): Revision Note

Percentage change

How do I find a percentage change?

• The multiplier that was used for a percentage change can be found using the formula:

  • $m=\frac{\mathrm{Amount}\mathrm{after}}{\mathrm{Amount}\mathrm{before}}$

• The value of $m$ corresponds to the multiplier for the percentage change

  • 1.05 corresponds to an increase by 5%

  • 0.75 corresponds to a decrease by 25%

• Alternatively you can use the formula:

  • Percentage Change = $\frac{\mathrm{After}-\mathrm{Before}}{\mathrm{Before}}\times 100$

  • A positive value is a percentage increase

    • An answer of 12 means an increase of 12%

  • A negative value is a percentage decrease

    • An answer of -28 means a decrease of 28%

How do I find a percentage profit or loss?

• Similar strategies to the above can be used to find the percentage profit or loss

• Shops buy or produce items at a "cost price" and sell them at a "selling price"

• Using a multiplier method:

  • $m=\frac{\mathrm{Selling}\mathrm{Price}}{\mathrm{Cost}\mathrm{Price}}$

  • 1.05 corresponds to a 5% profit

  • 0.75 corresponds to a 25% loss

• Alternatively you can use the formula:

  • Percentage Profit = $\frac{\mathrm{Selling}\mathrm{Price}-\mathrm{Cost}\mathrm{Price}}{\mathrm{Cost}\mathrm{Price}}\times 100$

  • A positive value is a profit

    • An answer of 12 means a 12% profit

  • A negative value is a loss

    • An answer of -28 means a 28% loss