Reverse Percentages | Questions and Worksheets | MME

# Reverse Percentages

Level 4 Level 5

## What you need to know

### Reverse Percentages

Reverse percentages are where we are given a value or an amount that has increased or decreased by a certain percent, we have to use this information to then calculate the original amount. There is a set method for calculating reverse percentages, you just need to know when to use it, often the trickiest part for students is spotting it is a reverse percentage question.

The steps to finding a reverse percentage are:

1. Either add or subtract the percentage given in the problem from 100% to determine what percentage we have
2. Find 1% of the amount by dividing by the percentage found in step 1
3. Find 100% (original amount) by multiplying your answer in step 2 by 100

Covering the following topics will help with understanding reverse percentages

### Take Note:

Often with reverse percentage questions they will gives some values and you will have to workout what you need to do, they won’t state ‘this is a reverse percentage question’. If the question gives you a percentage and a value then asks you to calculate a value from the past or the original amount, then it is likely to be a reverse percentage question. See the examples below.

### Example 1: Reverse Percentage

A TV cost £160 in a 20% off sale. Calculate the original price of the TV before the sale.

80% = £160

Divide both sides by 80 to find 1%

1% = £2

Then multiply by 100 to find 100%, i.e. the original amount

100% = £200

### Example 2: Reverse Percentage

A gyms membership increased in price by 15% to £23 a month. What was the cost of the membership before the increase?

115% = £23

Divide both sides by 115 to find 1%

1% = £0.20

Then multiply by 100 to find 100%, i.e. the original amount

100% = £20

### Example 3: Reverse Percentage

Rogelio’s new record for the 100m sprint is 10.8 seconds. This is 5.8% shorter than his previous record. What was his previous record (to 2dp)?

94.2% = 10.8 seconds

Divide both sides by 94.2 to find 1%

1% = 0.11464

Then multiply by 100 to find 100%, i.e. the original amount

100% = 11.46 (to 2 dp)

Note:With percentages you can always do a quick check to ensure your answer makes sense for the question given. In this case it is a percentage decrease from a previous value and so we would expect that previous value to be higher, which our answer is and tells us we haven’t made a silly mistake.

### Example Questions

To find the original price of the t-shirt we can divide the new cost by 0.75,

$£13.50\div0.75=£18$

To find the original cost of the car we can divide the new cost by 1.05,

$£15,550\div1.05=£14,761.90$

To find the total mass of the bar we can divide the mass of protein by 0.18,

$15.6g\div0.18=86.67g$

To find the total capacity of the stadium we can divide the recent attendance by 0.85,

$46,235\div 0.85 =54,394$

To find the total population of the U.K. we can divide the population of London by 0.14,

$9,300,000\div 0.14 =66,428,571$

Level 4-5

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