Profit, loss, and discount
Translate everyday buying and selling language into accurate amounts and percentages.
Identify the amounts#
Cost price is what the seller paid. Selling price is what the customer pays. Profit occurs when selling price exceeds cost price:
profit = selling price - cost price.
Loss occurs when cost price exceeds selling price.
Percentage base#
Profit percentage and loss percentage usually compare the change with cost price. If an item costs 800 and sells for 920, profit is 120 and profit percentage is 120 ÷ 800 × 100 = 15%.
Marked price and discount#
A discount is normally calculated from the marked or original price. A 20% discount on 1,500 is 300, so the sale price is 1,200.
The discount percentage and profit percentage can use different bases. Do not combine them until the actual amounts are known.
Successive changes#
A 20% discount followed by a further 10% discount is not a 30% reduction. Starting from 1,000 gives 800, then 720. The total reduction is 28%.
Common mistakes#
Avoid using selling price as the base for ordinary profit percentage unless the question explicitly defines a margin on sales. Also distinguish markup from profit: markup may be applied before discounts, while profit depends on the final selling price.
Reasonableness#
Write the base beside every percentage. Then calculate the amount and reconstruct the final price. The relationship cost + profit = selling price, or selling price + loss = cost, provides a useful check.
Key points
- Profit equals selling price minus cost price; loss reverses that difference.
- Profit and loss percentages normally use cost price as the base.
- Discount is measured from the marked or original price.
- Successive percentage changes should be applied one after another, not simply added.