# Reverse Percentages

## Reverse Percentages Revision

**Reverse Percentages**

Finding the **original value** before a percentage change has been applied is called a **reverse percentage**.

Once you are able to recognise it is a reverse percentage question, the method is very simple.

**Method 1: Calculating 1\%**

- Write the amount given
**as a percentage of the original amount**. - Find 1\% of the original amount by
**dividing**by this value - Multiply by \textcolor{#aa57ff}{100}

**Example:**

The price of a pair of trainers has been **decreased** by 20\%.

If its new price is £60.80, work out its **original price**.

- The trainers have been
**decreased**by 20\%, so £60.80 represents \textcolor{#10a6f3}{80\%} of its original value. **Divide**by 80 to find 1\% of the original price.**Multiply**by \textcolor{#10a6f3}{100}

£60.80 \div80=£0.76 (1\%)

£0.76\times 100=\textcolor{#10a6f3}{£76} (original price)

**Method 2: Using Decimals**

If you are comfortable with the method described above, you may find it easier to skip step 2 and 3.

This can be done by **converting the percentage** found in step 1 into a **decimal **and dividing by this value instead.

**Example:**

The value of a painting has **increased **by 30\% over the course of a year to £858.

Work out the value of the painting a year ago.

- £858 represents \textcolor{#10a6f3}{130\%} of the original value of the painting.
**Convert**this**percentage to a decimal**: 130\%=\textcolor{#10a6f3}{1.3}**Divide**by 1.3

£858 \div 1.3=\textcolor{#10a6f3}{£660}

**Example**

As part of a black Friday deal a laptop has been **reduced** by \textcolor{#10a6f3}{28\%} to £547.20.

Calculate the **original price** of the laptop before the discount.

**[2 marks]**

First find what percentage of the original price £547.20 is.

100\%-28\%=\textcolor{#10a6f3}{72\%}**Convert** to a decimal:

**Divide** the new price by this decimal:

£547.20 \div 0.72=\textcolor{#10a6f3}{£760}

## Reverse Percentages Example Questions

**Question 1:** The value of a car depreciates by 30\% one year after Erin bought it.

If the value of the car is now £5880, how much did she buy the car for?

**[2 marks]**

£5880 is 70\% of the original value of the car.

Original value =£5880\div 0.7=£8400

**Question 2:** The population of a town increases by 3.4\% every year.

The town’s population was 55319 in 2021, what was the population of the town in 2020?

**[2 marks]**

55319 represents 103.4\% of the population of the town in 2020.

Population of the town in 2020 =55319 \div 1.034=53500

**Question 3:** A striker for a football team scores 27 goals in one season, which is 30\% of the team’s total goals for that season.

Calculate the total number of goals scored by the football team in that season.

**[2 marks]**

27 goals represents 30\% of the team’s total goals.

Total number of goals =27\div 0.3=90