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Let cost price of an item be $C$, selling price be $S$. Assume the seller makes a profit.

Then profit would be: $P = S - C$.

Now, what is the formula for calculating Profit Percentage?

  1. $P \% = \dfrac{P}{C} \times 100$
  2. $P\% = \dfrac{P}{S} \times 100$

Which one is right and why?

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up vote 3 down vote accepted

The percentage profit $X$ is defined by

$$X = \left(\frac{\textrm{Amount of money you have at the end}}{\textrm{Amount of money you had at the start}} - 1\right) \times 100$$

Since you have $S$ at the end and $C$ at the start (because that's the money you needed to buy the item) then

$$X = \left( \frac{S}{C} - 1\right)\times 100 = \left(\frac{S-C}{C}\right)\times 100 = \frac{P}{C} \times 100$$

To see why your second decision has to be wrong, consider the case where you buy something for \$1 and sell it for \$1,001, so that $P$=1000. With your first definition,

$$X = 100\times \frac{1000}{1} = 100,000\%$$

which makes sense - you clearly made a huge profit, so you expect your percentage profit to be huge. With your second definition,

$$X = 100\times \frac{1000}{1001} = 99.9\%$$

which is nowhere near big enough.

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given (p/c)*100 what happens if your cost is 0? – chovy Nov 12 '13 at 7:07
You make infinite return. – Chris Taylor Nov 15 '13 at 13:57

They are both right.

The first expresses the profit as a percentage of the cost price. This is the profit mark-up.

The second expresses the profit as a percentage of the sales price. This is the profit margin.

Percentage profit on its own doesn't mean anything unless you are talking mark-up or margin. By convention, in a module I teach, percentage profit means profit mark-up.

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$C : S = 100 : (100+x) \Rightarrow 100\cdot S=100 \cdot C +C \cdot x \Rightarrow x=\frac {100(S-C)}{C}\Rightarrow x= \frac{100\cdot P}{C}$

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You say that 1st one is correct, i.e. we should measure the Profit percent wrto the Cost Price. Thank you. – Sai Manoj Kumar Yadlapati Feb 3 '12 at 13:36
@ysaimanojkumar,I guess that it is natural way of thinking... – pedja Feb 3 '12 at 13:38

answer two is right because : Suppose Cost of your product is 5400 Selling price is 8000 then profit is 2600

According to 2nd formula P%=P/S×100 profit % = 2600/8000 X 100 = 32.5%

Let's check profit according to 32.5%

profit = Selling price X profit % /100 8000 X 32.5% / 100 = 2600

hence formula 2nd is right

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Hello, welcome Mathematics.SE! Unfortunately, your answer is not correct; please see the accepted answer for explanation and intuition. It may be advisable to delete your answer, this can be done via the link on the bottom left. – Lord_Farin Jun 20 '13 at 13:15
@Lord_Farin I've imagined you saying that with the Portal's robotic voice. – Voyska Jun 20 '13 at 13:26

protected by T. Bongers Jul 1 '14 at 7:26

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