Question

A particular style of earrings costs the retailer $80 per pair. At what price should the retailer mark them so he can sell them at a 20% discount off the original price and still make 20% profit on his cost?

Answer 1

Percentages

The cost of the pair of earrings is $80 for the retailer. If it's sold at a 20% profit, then the price should be:

80 + 80 * 20 / 100 = 80 + 16 = $96

But the retailer wants to fake a 20% discount, so he must raise the price even more.

To make this last price 20% discount of the new price, it should be 80% (0.80) of that new price, thus we can calculate:

Final price = $96 / 0.80 = $120

Let's test our answer. The final price is $120, the buyer gets a 20% discount, thus the pays:

120 - 120 * 20 / 100 = 120 - 24 = $96

And this is exactly the price that gives us 20% profit on the original cost of $80.