# 2.1 Calculating a result following a percentage increase or decrease

In this section you will concentrate on how to find out the result of a percentage increase and decrease. Like lots of things in maths, there’s more than one way of working this out. The way shown here is designed to make some of the later sections this week easier.

Let’s see how it works with a couple of examples.

A coat originally priced at £80 is now in the sale with 30% off. What is the new sale price?

The original price was £80. That corresponds to 100%. It now has 30% off, so that means you are left with 100% − 30% = 70%. Therefore, to find out how much the coat costs now, you need to find 70% of £80.

To do that, you need to multiply £80 by , so

which can be cancelled down to leave .

Now take a look at an example of a percentage increase.

In 2012, a house was sold for £180 000. Its value has now increased by 35%. What is it now worth?

The house started at £180 000 which corresponds to 100%. It’s worth 35% more so the price now corresponds to 135%.

To find its current price you need to find 135% of £180 000. To do that, you need to multiply £180 000 by so

which can be cancelled down to leave .

Now have a go yourself.

## Activity 5 Percentage increases and decreases

- A type of chocolate used to come in 200g bars. The new bars are 15% smaller than the old ones. How big are the new bars?

### Answer

The new chocolate bar is 100% – 15% = 85% the size of the old one. To work out the size of the new bar, you therefore need to find 85% of 200g.

- In an old job I earnt £25 000 a year. In my new job I earn 10% more. What do I earn now?

### Answer

The new pay is 100% + 10% = 110% of the old pay. So to work out the new pay, you need to find 110% of £25000.