Skip to content
Skip to main content

About this free course

Download this course

Share this free course

Succeed with maths: part 1
Succeed with maths: part 1

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

2.3 Calculating original amounts

A situation that can be a little tricky to understand is how to undo a percentage change that has been added to or subtracted from a number. The video below will show how to work this out, again using an example with discounts and VAT.

Download this video clip.Video player: swm_1_s6_calculating_original_amount_animation.mp4
Copy this transcript to the clipboard
Print this transcript
Show transcript|Hide transcript
Interactive feature not available in single page view (see it in standard view).

From the video, you can check your answer by working out the 5 per cent postage charge on £28.57 to see that the grand total will be £30.

Many people in this situation may think that they can work out 5 per cent of £30 and subtract this from the £30 to find out how much they can spend. Try this now.

5% of £30 = 0.05 × £30 = £1.50

£30 – £1.50 = £28.50

This answer is 7p less than using our other method! So something must be wrong.

The reason for this is because this is all to do with what it’s 5% of! 5% of different numbers gives a different answer. The 5% added here is 5% of £28.57. 5% of £30 isn’t the same as 5% of £28.57 – it’s a bigger number.

This is an important idea to remember. Have a go at this in the next two activities.

Activity 7 What was the price before VAT?

Timing: Allow approximately 10 minutes

The price of a tennis racquet, including 20 per cent VAT, is £45.24. What was the price before VAT?

Hint: the £45.24 includes VAT. What percentage does this total represent? Find the monetary amount that represents 1 per cent, and use that figure to arrive at 100 per cent.


The price before VAT was added is the original 100 per cent.

So £45.22, which includes VAT, is equivalent to 120 per cent of the cost (100% + 20%).

1 per cent of £45.24 = £45.24 ÷ 120

Original cost left parenthesis 100 percent right parenthesis equals one per cent of pound 45 .24 prefix multiplication of 100 equals pound 45.24 divided by 120 multiplication 100 percent equals prefix pound of 37.70

Thus, the price of the tennis racquet before VAT was applied was £37.70.

Activity 8 What was the original price before a sale?

Timing: Allow approximately 10 minutes

I saw a coat in a sale. Its sale price was advertised as £64, which was after a 20% discount.

Unfortunately, I wasn’t able to buy it in the sale – the sale was ending soon and I’d not yet been paid that month.

However, as I really liked the coat, I thought I might buy it anyway at full price once I’d been paid. How much would it cost me when not in the sale?


The price before the sale is the original 100 per cent.

In the sale, 20% was taken off. That means 80% was left. So £64 is 80%.

You can work out what 1% is by doing £64 ÷ 80 = £0.80

Based on this, 100% is 100 × £0.80 = £80. So, the price of the coat when it’s not in the sale is £80.

You have very nearly finished your work on percentages for this week, but before you move onto ratios you’re going to take a quick look at the idea of percentage points. You may have heard or read about these in news reports, but not really thought about what these mean. Now it’s your chance to find out about the important difference between percentages and percentage points.