  # Calculating Reverse Percentages

In this worksheet, students will practise how to use reverse percentages in given scenarios. Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Solve Problems Involving Percentage Change

Difficulty level:   #### Worksheet Overview

Have you ever noticed how the 'sale' sign almost has a magnetic effect on shoppers? You may have found yourself drawn to such an aisle in a store and found yourself picking up items you really don't need because the helpful little sign informs you that it is '20% off'.

Does this sound familiar?

In this situation, it'd be really helpful to know what the original cost of the item was as this would allow us to work out if it's worth splashing the cash.

Let's take the following example: In a sale, it is 40% off all prices. You pay £120 for a tv. How much was
the tv before the sale?

1) We know that the price listed must, therefore, be 60% of the total cost.
100 % (Original Cost) 40 % (Sale amount) 60% (This is how much the tv is currently worth of the original price)

2) We should now set this up as a ratio, using the following structure:

£ : %

When we input the numbers here we get:

£120 : 60 %

3) We now have your ratio set up, we now need to find out how much the original cost was/ or 100%. The easiest thing to do is divide both sides by the percentage to find 1%,
then multiply both sides by 100.

£120 : 60%

(÷ both sides by 60) This gives us the ratio:

2:1

(× both sides by 100) This will give us 100% of the original cost of the tv:

£200 : 100 %

So, there we have our answer.  Seems, like that was quite a good bargain after all!

In this activity, that's exactly what we'll be doing.  We'll be recapping how to reverse the percentages, so that we can work out if these 'bargains' are really worth it.

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