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# Reverse percentage problems (original amount percentage questions)

A reverse percentage is where you need to go back in time to find the original amount. First, you will need to identify that the question is a reverse percentage question. Look out for questions like what did the item cost before the sale? Once this is done, you need to add the percentage to 100 if the question is a percentage increase question or take the percentage off 100 if it’s a percentage decrease question. Make this percentage equal to the amount in the question. All you need to do next is work out the value of 100% as this is the original amount. Do this by working out 1% and then multiplying by 100.

This is probably one of the trickiest percentage problems to master, so let’s take a look at a couple of questions on reverse percentage problems.

**Example 1**

A laptop computer is reduced by 20% in a sale and is now worth $520. How much did the laptop cost before the sale?

First you need to realise you need to find the original cost of the laptop (so it is a reverse percentage problem).

Taking 20% off 100% you get 80% (as the question is a percentage decrease question).

Therefore, 80% = $520.

Now work out 1% by dividing by 80:

Therefore, 1% = $6.50

Next find 100%, as 100% is the original amount. Do this by multiplying by 100:

100% = $650.

So the laptop was $650 before the discount.

You can check this answer is correct by deducting 20% off $650.

**Example 2**

A tree grows 8% taller since last year and is now 4.5 metres tall. What was the height of the tree last year?

Again, you need to realise you need to find original height of the tree (so it’s a reverse percentage problem).

Adding 8% to 100% you get 108% (as the question is a percentage increase question).

Therefore, 108% = 4.5.

Now work out 1% by dividing by 108:

Therefore, 1% = 0.0416666...

Next find 100%, as 100% is the original amount. Do this by multiplying by 100:

100% = 4.17m.

So the tree was 4.17m tall before the increase.

You can check this answer is correct by working out 8% of 4.17 and adding it back on to 4.17.

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