Name: Sally

Who is asking: Other

Level: Middle

Question:

If 20% of 100 is 80, then why is the percentage difference between 80 and 100 25%.

Hi Sally,

Percent means per one-hundred so 20% of 100 is

^{20}/_{100} x 100 = 20.
Likewise 20% of 60 is
^{20}/_{100} x 60 = 12.
The second part of your question raises another problem. When you ask a percentage question you need to ask **percentage of what**. When you say the difference between 80 and 100 is 25% you need to say **25% of what**. Consider this example. You buy an item for $80 and you want to mark it up to sell it. If you mark it up 25% (that is 25% of what it cost you) then you mark it up

^{25}/_{100} x $80 = $20.
and sell it for $80 + $20 = $100. In this example the difference between $100 and $80 is 25% of $80.
As a second example suppose that a shop owner has an item which sells for $100. She decides to put it on sale for $80, and thus marks it down $20. In this case she would say **reduced by 20%.** Here she means that the price has been reduced by 20% of the original price of $100.

I hope this helps,

Penny