5.1 Percentage increases and decreases
You’ll often see percentage increases and decreases in sales and pay rises.
Example: Anjali’s pay rise
Anjali earns £18,000 per year. She is given a 10% pay rise. How much does she now earn?
In order to identify Anjali’s new salary, you need to find out what 10% () of £18,000 is. To do this, first you need to find out of £18,000:
18,000 ÷ 100 = 180
So of £18,000 is:
10 × 180 = 1,800
Anjali’s pay rise is £1,800, so her new salary is:
£18,000 + £1,800 = £19,800
Example: A sale at the furniture shop
A residential care home is undergoing a refurbishment and purchasing new bedroom furniture for the residents. They find a furniture shop that has reduced all of its prices by 20%. How much does a £300 double bed cost in the sale?
In order to identify the new price of the double bed, you need to find out what 20% () of £300 is. To do this, first you need to find out of £300:
300 ÷ 100 = 3
So of £300 is:
20 × 3 = 60
The discount is £60, so the sale price of the double bed is:
£300 – £60 = £240
Use the examples above to help you with the following activity. Remember to check your answers once you have completed the questions.
Activity 16: Calculating percentage increases and decreases
- A brand new ambulance costs £90,000. Its value depreciates (decreases) by 25% annually. How much will the ambulance be worth at the end of the first year?
- Between 2014 and 2017 the number of patients suffering from mental health conditions who were sent away from their homes, to other towns and cities, for treatment increased by 40%. If 4,000 patients received treatment away from their local area in 2014, how many were treated away from home in 2017?
- In order to identify how much the value of the ambulance will decrease by, you need to find out what 25% () of £90,000 is. To do this, first you need to find out of £90,000:
- 90,000 ÷ 100 = 900
- So of £90,000 is:
- 25 × 900 = 22,500
- The ambulances’s value depreciates by £22,500 in the first year, so the value of the ambulance at the end of the first year will be:
- £90,000 – £22,500 = £67,500
- In order to identify how many patients were treated away from home in 2017, you need to find out what 40% () of 4,000 is. To do this, first you need to find out of 4,000:
- 4,000 ÷ 100 = 40
- So of 4,000 is:
- 40 × 40 = 1,600
- The number of patients has increased by 1,600 since 2014, so the number of patients in 2017 is:
- 4,000 + 1,600 = 5,600
5,600 patients received treatment away from their local area in 2017.
In this section you have learned how to calculate percentage increases and decreases. This will be useful when working out the value of a pay increase or how much medical items will cost after a price reduction. You have also seen, and successfully used, two methods of calculating a percentage. There is one method that you haven’t been shown (and it’s probably the easiest!): using the percentage button on your calculator. The percentage button looks like this:
To successfully use it when calculating percentages you would enter the sum into your calculator as follows.
If you were asked to find 20% of 80, on your calculator you would input:
- 80 × 20%
This would give you the following answer:
- 80 × 20% = 16
This is by far the easiest way of calculating percentages when you have a calculator handy.
In this section you have learned how to solve problems using percentages, and how to calculate percentage increases and decreases.