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%.

• The 10% Additional Discount

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%.