IGCSEMaths: CoreCIERevision NotesNumberPercentages ToolkitPercentage Change

Syllabus Edition

First teaching 2023

First exams 2025

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Percentage Change (CIE IGCSE Maths: Core)

Revision Note

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Jamie W

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Jamie W

Expertise

Maths

Percentage Increases & Decreases

How do I increase by a percentage?

  • A percentage increase makes an amount bigger by adding that percentage on to itself
  • Without a calculator, use the methods outlined in Basic Percentages to find the percentage you are increasing by
  • Then add this on to the original amount 
    • To increase 30 by 10%
      • 10% of 30 is 3
      • 30 + 3 = 33
      • This is equivalent to finding 110% of 30
  • With a calculator it is more efficient to use multipliers
    • A multiplier is the decimal equivalent of a percentage
      • A percentage can be converted to a decimal by dividing by 100
    • When increasing by a percentage, we are finding a percentage greater than 100%
    • To increase 80 by 15%
      • We are finding 115% of 80, so the multiplier is 1.15
      • 1.15 × 80 = 92

How do I decrease by a percentage?

  • A percentage decrease makes an amount smaller by subtracting that percentage from itself
  • Without a calculator, use the methods outlined in Basic Percentages to find the percentage you are decreasing by
  • Then subtract this from the original amount 
    • To decrease 30 by 10%
      • 10% of 30 is 3
      • 30 - 3 = 27
      • This is equivalent to finding 90% of 30
        • Because 100% - 10% = 90%
  • With a calculator it is more efficient to use multipliers
    • When decreasing by a percentage, we are finding a percentage smaller than 100%
    • To decrease 80 by 15%
      • We are finding 85% of 80, so the multiplier is 0.85
        • Because 100% - 15% = 85%
      • 0.85 × 80 = 68

Worked example

(a)

Increase 200 kg by 21%

Non-calculator method
By first finding 10% and 1%, find 21% of 200

10% of 200 = 20
1% of 200 = 2
21% of 200 = 20 + 20 + 2 = 42 

Add this to the original amount

200 + 42

242 kg

Calculator method
An increase by 21% is equivalent to finding 121% of the original amount
So the multiplier is 1.21 

1.21 × 200

242 kg

 

(b)

An item that costs $ 500 is discounted by 35%. Find the new price of the item.

A discount of 35% means the price decreases by 35%

Non-calculator method
By first finding 10% and 5%, find 35% of 500 

10% of 500 = 50
5% of 500 = 25
35% of 500 = 50 + 50 + 50 + 25 = 175 

Subtract this from the original amount

500 - 175

$ 325

Calculator Method
A decrease of 35% is equivalent to finding 65% of the original amount (100 - 35 = 65) 
So the multiplier is 0.65

500 × 0.65

$ 325

 

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 equals fraction numerator Amount space after over denominator Amount space before end fraction
  • 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 = fraction numerator After space minus space Before over denominator Before end fraction cross 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 equals fraction numerator Selling space Price over denominator Cost space Price end fraction
    • 1.05 corresponds to a 5% profit
    • 0.75 corresponds to a 25% loss
  • Alternatively you can use the formula:
    • Percentage Profit = fraction numerator Selling space Price space minus space Cost space Price over denominator Cost space Price end fraction cross 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

Exam Tip

  • 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.

Method 1
Use the formula m equals fraction numerator Amount space after over denominator Amount space before end fraction

310 over 250 equals 1.24 

This multiplier corresponds to an increase of 24%

A percentage increase of 24%

Method 2
Use the formula Percentage Change = fraction numerator After space minus space Before over denominator Before end fraction cross times 100

fraction numerator 310 minus 250 over denominator 250 end fraction cross times 100 equals 24

The value is positive, so this is a percentage increase

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. 

Method 1
Use the formula m equals fraction numerator Selling space Price over denominator Cost space Price end fraction

5600 over 8000 equals 0.7

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

A loss of 30%

Method 2
Use the formula Percentage Profit = fraction numerator Selling space Price space minus space Cost space Price over denominator Cost space Price end fraction cross times 100

fraction numerator 5600 minus 8000 over denominator 8000 end fraction cross times 100 equals negative 30

The value is negative, so this is a percentage loss

A loss of 30%

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    Jamie W

    Author: Jamie W

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.