Name: Sally

Who is asking: Other
Level: Middle

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,

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