Profit, Loss & Price Changes (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Profit, Loss & Price Changes

How do I calculate profit and loss?

• If you purchase an item and then sell it for more than you paid, you make a profit

  • If you sell it for less than you paid, you make a loss

• The difference between the selling price and the cost price is the profit

  • Selling price - cost price = profit

  • If this is positive, it is a profit

  • If this is negative, it is a loss

• This could be expressed as an amount in pounds, or as a percentage

  • To find the percentage profit, divide the profit by the cost price and express as a percentage

  • i.e.

• There may be other costs involved too, which should be taken into account when calculating the profit

• When a business calculates its profit they may use the term revenue

  • Revenue is the total income a business earns

  • Profit = total revenue - total costs

  • E.g. In a coffee shop, revenue is all the money customers pay over a period of time

    • To find the profit, subtract all the costs of running the shop (such as beans, cups, milk, rent, and staff wages) from that revenue

How do I calculate price increases and decreases?

• When dealing with price increases and decreases, use a multiplier

  • To increase by 32% use ×1.32

  • To decrease by 32% use ×0.68

    • This is 1 - 0.32

• E.g. If a coat usually costs £50 but receives a 15% discount

  • The new price will be 50×0.85 = £42.50

What if there are multiple increases and decreases?

• If there is a repeated increase or decrease by the same percentage, you can use a power

  • This is the same as when calculating with compound interest

• E.g. If the price of a bus ticket was £3.20 which then increases by 3% one year, and by 3% again the following year

  • The new price after the 2 years will be 3.20×1.03² = £3.39

• If there are multiple price changes by different percentages, use several multipliers

• E.g. If a shop raises the price of a pair of trainers costing £40 by 5% and then discounts them by 20%

  • The new price will be 40×1.05×0.8 = £33.60