Percentage Change (Cambridge International IGCSE Maths)

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 = $\frac{\mathrm{After}-\mathrm{Before}}{\mathrm{Before}}\times100$

  • 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 = $\frac{\mathrm{Selling} \mathrm{Price}-\mathrm{Cost} \mathrm{Price}}{\mathrm{Cost} \mathrm{Price}}\times100$

  • 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

Exam Hint Use "common sense" to check your answer!

If an item is sold for more than it was bought for, you are expecting a profit, not a loss.

Worked Example The number of students in a school changes from 250 to 310. Describe the percentage change in number of students.

Answer:

Method 1 Use the formula $m=\frac{\mathrm{Amount} \mathrm{after}}{\mathrm{Amount} \mathrm{before}}$

$\frac{310}{250}=1.24$* *

This multiplier corresponds to an increase of 24%

Final answer: A percentage increase of 24%

Method 2 Use the formula Percentage Change = $\frac{\mathrm{After}-\mathrm{Before}}{\mathrm{Before}}\times100$

$\frac{310-250}{250}\times100=24$

The value is positive, so this is a percentage increase

Final answer: A percentage increase of 24%

Worked Example Sophie purchases a car for £8000 and sells it several years later for £5600. Describe the percentage profit or loss on the car.

Answer:

Method 1 Use the formula $m=\frac{\mathrm{Selling} \mathrm{Price}}{\mathrm{Cost} \mathrm{Price}}$

$\frac{5600}{8000}=0.7$

This means the selling price was 70% of the cost price, so a loss of 30%

Final answer: A loss of 30%

Method 2 Use the formula Percentage Profit = $\frac{\mathrm{Selling} \mathrm{Price}-\mathrm{Cost} \mathrm{Price}}{\mathrm{Cost} \mathrm{Price}}\times100$

$\frac{5600-8000}{8000}\times100=-30$

The value is negative, so this is a percentage loss

Final answer: A loss of 30%