# Math Help - Percentage increase / decrease eplanation

1. ## Percentage increase / decrease eplanation

Hi

I am trying to explain how the following works. If a object costs £100 the shop increase it by 5% so it is now £105.
The shop then reduce it from £105 buy 10% in a sale and now being £94.50.
Why is this different to the original £100 and the 5% being taken of this which would be £95.
So basically why is increasing something by 5% then reducing by 10% not the same as reducing the original by 5%

I can do the math behind these calculations, im just confused how to explain why there is a difference.

regards

2. ## Re: Percentage increase / decrease eplanation

Consider an easier example.
Suppose a $100 item is increased by 10% and subsequently reduced by 10%. The resulting price is$99.
10% of 110 is greater than 10% of 100 so the reduction is greater than the raise.

3. ## Re: Percentage increase / decrease eplanation

The amount of a percent change depends upon the base. 5% of a larger amount will be larger than 5% of a smaller amount. When you added 5% to the orginal price, you increased the base.