Math CentralQuandaries & Queries


Question from Anson, a student:

The cost price of a CD is $\$50$ and its marked price is $\$105.$ If the selling price is $\$88,$ find the profit percent.

Hi Anson,

If the cost price is $\$50$ and the selling price is $\$88$ then the profit is $\$88 - \$50 = \$38.$ The problem in expressing this as a percentage is the necessity to ask "percentage of what?"

From the seller's point of view he bought the item for $\$50$ and sold it for $\$88$ so his profit is $\large \frac{\$33}{\$50} \times \normalsize 100 = 66\%$ of what it cost him.

From the buyer's point of view he paid $\$88$ so the profit of $\$38$ is $\large \frac{\$38}{\$88} \times \normalsize 100 = 43.2\%$ of what he paid for it.

I hope this helps,

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