# If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage?

If the 10% discount is given instead of the original 25% discount, then the new profit percentage is 30%. If, however, the 10% discount is given on top of the original 25%, then the profit percentage is reduced to 22.5%. How to arrive at these figures is detailed below.

• The 10% Alternative Discount
Assuming that the original selling price is \$100, the first step is to determine the selling price at a 25% discount. As 25% of 100 equals \$25, the new selling price is \$100 minus \$25, which makes it \$75.

A discount of 10% would result in a new selling price of \$90, as 10% of \$100 equals \$10.

A selling price of \$75 resulted in a 25% profit. By determining the profit percentage to selling price ratio, and multiplying the result by the new selling price, the new profit percentage can be determined. To do this here, the 25% profit is divided by \$75, then multiplied by \$90. The result is therefore 25% / \$75 x \$90, which equals 30%.

If the 10% discount is to be taken off on top of the original 25%, the new profit percentage can be worked out as follows:

\$100 minus 25% equals \$75
\$75 minus 10% equals \$75 minus \$7.50, which results in a new selling price of \$67.50.
The new profit percentage can now be worked out as before, namely by dividing the original profit percentage of 25% by \$75, then multiplying by the new selling price, \$67.50. So the new percentage of profit is 25% / \$75 x \$67.50, which equals 22.5%.

• Profit on Full Price
So how much profit is the company making on the full price of \$100? It is simple: 25% / \$75 x \$100, which makes 33.33%.
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