Math CentralQuandaries & Queries


Question from ata:

My cost is 100 and I want to make 20% profit on my selling price (not 20% of the cost). So, what should be calculation formula? Let's say my cost is 493.71 and I want to make 53.28% profit on the selling price; so how to determine the selling price?

Hi Ata,

Some algebra helps solve this. Suppose your cost is $\$C$ and the selling price is $\$S,$ your profit is then you want your $\$S - \$C.$ You want your profit to be 20% of your selling price so what you need is

\[\$S - \$C = 0.20 \times \$S.\]

Add $C to each side to obtain

\[\$S = 0.20 \times \$S + \$C\]

and then subtract 0.20 × $S from each side to get

\[\$S - 0.20 \times \$S = \$C.\]


\[0.80 \times \$S = \$C\]

or, dividing both sides by 0.80

\[\$S = \frac{\$C}{0.80}.\]

Hence for the example you sent, if the cost is $\$C = \$100$ then

\[\$S = \frac{\$100}{0.80} = \$125.\]

I hope this helps,

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