The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Reversed Percentages

In this worksheet, students use percentage multipliers to work out the original price after a percentage increase or decrease.

'Reversed Percentages' worksheet

Key stage:  KS 4

Curriculum topic:  Ratio, Proportion and Rates of Change

Curriculum subtopic:  Set Up, Solve and Interpret Answers in Growth and Decay Problems

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Percentage multipliers are useful as a quick way to work out percentage increases and decreases. 

 

They can also be used to work out the original quantity after a percentage increase or decrease.  Here we divide by the percentage multiplier to find the original amount.

 

To find the orginal amount:

after a percentage increase

Divide by 1 + percentage as a decimal

 

A 5% increase is the equivalent of a percentage multiplier of 1.05

 

after a percentage decrease

Divide by 1 - percentage as a decimal

 

A 5% decrease is the equivalent of a percentage multiplier of 0.95

 

Example 1

A table costs £300 after 20% VAT has been added.  What did it cost before VAT?

 

Answer

The multiplier was 1 + 0.20 = 1.20 or 1.2

Answer is £300 ÷ 1.2 = £250

 

Example 2

A tennis racket costs £76.50 in a 15% sale.  What did it cost before the discount was applied?

 

Answer

The multiplier was 1 - 0.15 = 0.85

Answer is £76.50 ÷ 0.85 = £90

Use a percentage multiplier to calculate the original price.

 

A child's car seat costs £68.25 after 5% VAT has been added.  What was its price before VAT?

£65

£68.25

£61.75

£65.50

Use a percentage multiplier to calculate the original price.

 

A car costs £11400 after 20% VAT has been added.  What was the price before VAT?

£1900

£9520

£9500

£11400

Use a percentage multiplier to calculate the original price.

 

A football costs £10.80 in a 10% sale.  What did it cost before the sale?

£12

£10.90

£10.80

£12.20

Use a percentage multiplier to calculate the original price.

 

A suitcase costs £36 in a 25% sale.  How much did it cost before the sale?

£9

£45

£60

£48

Use a percentage multiplier to calculate the original price.

 

A bicycle costs £180 after 20% VAT has been added.  How much did it cost before VAT?

£152

£150.20

£150

£180

Use a percentage multiplier to calculate the original price.

 

A leather handbag costs €70.40 in a 12% sale.  How much did it cost before the sale?

€82.40

€82

€70.52

€80

Use a percentage multiplier to calculate the original price.

 

A motorbike costs € 3050 after 22% VAT has been added.  How much did it cost before VAT?

€3000

€1950

€2522

€2500

Use a percentage multiplier to calculate the original price.

 

A clock costs €166.75 after 15% VAT has been added.  How much did it cost before VAT?

€145

€151.75

€168.25

€155

Use a percentage multiplier to calculate the original price.

 

A book costs £13.80 after an 8% discount.  How much did it cost before the discount?

£13.88

£15

£14

£13.80

Use a percentage multiplier to calculate the original price.

 

A picture costs £64.75 in a 12½% sale.  How much did it cost before the sale?

£74

£57.55

£64.75

£83.25

  • Question 1

Use a percentage multiplier to calculate the original price.

 

A child's car seat costs £68.25 after 5% VAT has been added.  What was its price before VAT?

CORRECT ANSWER
£65
EDDIE SAYS
£68.25 ÷ 1.05
  • Question 2

Use a percentage multiplier to calculate the original price.

 

A car costs £11400 after 20% VAT has been added.  What was the price before VAT?

CORRECT ANSWER
£9500
EDDIE SAYS
£11400 ÷ 1.2
  • Question 3

Use a percentage multiplier to calculate the original price.

 

A football costs £10.80 in a 10% sale.  What did it cost before the sale?

CORRECT ANSWER
£12
EDDIE SAYS
£10.80 ÷ 0.9
  • Question 4

Use a percentage multiplier to calculate the original price.

 

A suitcase costs £36 in a 25% sale.  How much did it cost before the sale?

CORRECT ANSWER
£48
EDDIE SAYS
£36 ÷ 0.75
  • Question 5

Use a percentage multiplier to calculate the original price.

 

A bicycle costs £180 after 20% VAT has been added.  How much did it cost before VAT?

CORRECT ANSWER
£150
EDDIE SAYS
£180 ÷ 1.2
  • Question 6

Use a percentage multiplier to calculate the original price.

 

A leather handbag costs €70.40 in a 12% sale.  How much did it cost before the sale?

CORRECT ANSWER
€80
EDDIE SAYS
€70.40 ÷ 0.88
  • Question 7

Use a percentage multiplier to calculate the original price.

 

A motorbike costs € 3050 after 22% VAT has been added.  How much did it cost before VAT?

CORRECT ANSWER
€2500
EDDIE SAYS
€3050 ÷ 1.22
  • Question 8

Use a percentage multiplier to calculate the original price.

 

A clock costs €166.75 after 15% VAT has been added.  How much did it cost before VAT?

CORRECT ANSWER
€145
EDDIE SAYS
€166.75 ÷ 1.15
  • Question 9

Use a percentage multiplier to calculate the original price.

 

A book costs £13.80 after an 8% discount.  How much did it cost before the discount?

CORRECT ANSWER
£15
EDDIE SAYS
£13.80 ÷ 0.92
  • Question 10

Use a percentage multiplier to calculate the original price.

 

A picture costs £64.75 in a 12½% sale.  How much did it cost before the sale?

CORRECT ANSWER
£74
EDDIE SAYS
£64.75 ÷ 0.875
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1