## 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:

- Either add or subtract the percentage given in the problem from 100% to determine what percentage we have
- Find 1% of the amount by dividing by the percentage found in step 1
- 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

**Question 1: **The price of a t-shirt is reduced by 25% to £13.50 during a sale. How much did it originally cost?

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

£13.50\div0.75=£18

**Question 2: **The price of a car has increased by 5% to £15,500. What was the cost of the car prior to this increase?

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

£15,550\div1.05=£14,761.90

**Question 3: **A sports recovery bar contains 15.6g of protein. 18% of the recovery bar is protein. Work out the total mass of the bar.

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

15.6g\div0.18=86.67g

**Question 4: **The crowd attendance at a recent football game is 46,235. This is 85% capacity of the ground. What is the total capacity of the stadium.

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

46,235\div 0.85 =54,394

**Question 5:** The population of London is 9,300,000. This represents 14% of the population of the United Kingdom. Work out the total population of the U.K.

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

### Worksheets and Exam Questions

#### (NEW) Reverse percentages Exam Style Questions

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