Discount Price (Percentage Off)

A percentage off multiplies the list price by what remains: 30% off $250 leaves $250 \ imes 0.70 = \$175$. Solved the other way, any pair of list and sale prices reveals the discount actually given, which is the useful direction when a supplier quotes you a net price and you want to know where you sit on their schedule.

Two things trip people up. Successive discounts do not add: 20% off followed by a further 10% off is $0.8 \ imes 0.9 = 0.72$, a 28% discount rather than 30%. And a discount is not the mirror of a markup. Marking $100 up by 50% gives $150, but taking 50% off $150 gives $75, not $100. To undo a markup you divide, and the equivalent discount is always the smaller percentage.