Hi ,

If you are a merchant and you bought an item for $54.00 and then sold it to a customer for $117.00 then you marked it up $63.00 (63 = 117 - 54). But you want to express this as a percentage.

When reporting a percentage you should always say percentage of what. From your perspective as the merchant you want to know "What is $63.00 as a percentage of what it cost me?" I think of this question as

$63.00 is what percentage of $54.00?

and then I can translate it into an equation. "Percentage" means per 100, that is over 100, "what" is the quantity I don't know so I will call it x, "of" is multiplication and "is" is the equal sign. Thus the question is

63.00 = ^x/₁₀₀ 54.00

Solving for x I get

x = ⁶³⁰⁰/₅₄ = 116.7

Hence $63.00 is 116.7% of $54.00. Thus the markup is 116.7% in the sense that the markup is 116.7% of what it cost the merchant.

From your customer's perspective the question might still be "What is $63.00 as a percentage of what it cost me?" but this time it means

$63.00 is what percentage of $117.00?

which becomes

63.00 = ^x/₁₀₀ 117.00

Solving for x this time gives

x = ⁶³⁰⁰/₁₁₇ = 53.8

Hence $63.00 is 53.8% of $117.00. Thus the markup is 53.8% in the sense that the markup is 53.8% of what it cost your customer.

So what is the percentage markup? This is a very ill formed question. If someone says to you that the markup is some percentage you need to ask "Percentage of what?" If you are reporting your markup you need to say "The markup is such and such percentage of my cost", and as a customer I need to say "The markup is such and such percentage of what it cost me".

I hope this helps,
Penny

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