Profit, loss & discount

The cost price is what you pay for something; the selling price is what you sell it for. Profit = selling price − cost price. If you buy a bike for $80 and sell it for $110, your profit is 110 − 80 = $30. If the selling price is lower than the cost, the result is a loss: buying for $60 and selling for $45 is a loss of 60 − 45 = $15.

A $10 profit means more on a cheap item than an expensive one, so we often compare profit to the cost price as a percentage: profit % = (profit ÷ cost) × 100. Buying candles for $50 and selling for $60 gives a $10 profit, which is (10 ÷ 50) × 100 = 20% of the cost. The same formula with a negative profit gives a percentage loss.

A discount is a percentage taken off the price. First find the discount in dollars — price × percent ÷ 100 — then subtract it. A $200 item at 10% off has a $20 discount, so the sale price is 200 − 20 = $180. A $250 bike at 20% off saves $50, leaving $200.

Shops add a mark-up to the cost so they make a profit. A mark-up is a percentage added to the price: new price = price + price × percent ÷ 100. A jacket bought for $120 and marked up 25% gains $30, so it sells for $150. Selling at “a 45% profit” works the same way — add 45% of the cost to the cost.

Each answer is an amount of money or a percentage. Type just the number — you can include a dollar sign if you like, but you don't need to.