Profit, Loss and GST
Profit, Loss and GST in NSW Year 8 maths (NESA outcome MA4‑FRC‑C‑01) compares the cost price a seller pays with the selling price a buyer pays, and adds or removes the 10% Goods and Services Tax.
You will find profit and loss in dollars and as a percentage of the cost price (or of the selling price when asked), apply a mark-up, add GST by multiplying by 1.1, and take it out of a GST-inclusive price by dividing by 1.1 or by finding the GST as the total \(\div\, 11\). Canteen pies, a surf shop’s caps, sneakers in a sale and a cafe’s burger meal show how businesses set their prices. It is part of Year 8 Fractions and Percentages.
Every question with a fully worked solution.
- Profit, Loss and GST - Video - Profit, Loss and GST 1 Watch
Theory
Profit \(=\) selling price \(-\) cost price, and a loss is cost price \(-\) selling price. As a percentage, divide by the cost price: buying for \(\$2400\) and selling for \(\$3000\) is a \(\dfrac{600}{2400} = 25\%\) profit. GST adds \(10\%\): multiply by \(1.1\). This Year 8 maths page shows how.
The two prices. The cost price is what the seller paid. The selling price is what the buyer pays.
In dollars. Profit \(=\) selling price \(-\) cost price. Loss \(=\) cost price \(-\) selling price. Both are written as positive amounts.
As a percentage. Percentage profit \(= \dfrac{\text{profit}}{\text{cost price}} \times 100\%\), and percentage loss uses the loss over the cost price. If a question asks for a percentage of the selling price, divide by the selling price instead.
Mark-up. Selling price \(=\) cost price \(+\) mark-up. A mark-up of \(25\%\) multiplies the cost price by \(1.25\): \(1.25 \times 60 = 75\). To go back to the cost price, divide by the multiplier.
GST (Goods and Services Tax) is \(10\%\) of the price before GST, added on top. Add GST by multiplying by \(1.1\).
GST inside a total. A GST-inclusive total is \(110\%\) of the price before GST, so the GST is the total \(\div\, 11\) and the price before GST is the total \(\div\, 1.1\).
Money to the cent, and round a percentage only as far as the question asks.
The formulas:
| To find | Use |
|---|---|
| profit | selling price − cost price |
| loss | cost price − selling price |
| percentage profit or loss | \(\dfrac{\text{profit or loss}}{\text{cost price}} \times 100\%\) |
| selling price after a \(p\%\) mark-up | cost price \(\times (100 + p)\%\) |
| price including GST | price before GST \(\times 1.1\) |
| GST inside a total | total \(\div 11\) |
| price before GST | total \(\div 1.1\) |
Percentage profit or loss
- Subtract to find the profit or loss in dollars.
- Divide by the cost price (unless the question names the selling price).
- Multiply by \(100\%\) and say whether it is a profit or a loss.
GST
- Adding GST: multiply the price before GST by \(1.1\).
- Inside a total: GST \(=\) total \(\div 11\); price before GST \(=\) total \(\div 1.1\).
(ii) Andy bought a painting for \(\$2400\) and sold it for \(\$3000\). What was the percentage profit?
| \(\text{Loss}\) | \(=\) | \(10\,500 - 8400\) |
| \(\) | \(=\) | \(2100\) |
| \(\text{Loss \%}\) | \(=\) | \(\dfrac{2100}{10\,500} \times 100\%\) |
| \(\) | \(=\) | \(20\%\) |
| \(\text{Profit}\) | \(=\) | \(3000 - 2400\) |
| \(\) | \(=\) | \(600\) |
| \(\text{Profit \%}\) | \(=\) | \(\dfrac{600}{2400} \times 100\%\) |
| \(\) | \(=\) | \(25\%\) |
(i) a \(20\%\) loss
(ii) a \(25\%\) profit
(ii) A TV sold for \(\$2343\) including GST. What was the price before GST?
(ii) The \(\$2343\) is \(110\%\) of the price before GST, \(p\).
| \(1.1 \times 12\,000\) | \(=\) | \(13\,200\) |
| \(\text{1\% of } p\) | \(=\) | \(2343 \div 110 = 21.3\) |
| \(\text{100\% of } p\) | \(=\) | \(21.3 \times 100 = 2130\) |
(i) \(\$13\,200\)
(ii) \(\$2130\). In one step: \(2343 \div 1.1 = 2130\).
(i) Find the profit on a punnet.
(ii) Find the percentage profit.
| \(4.25 - 2.50\) | \(=\) | \(1.75\) |
| \(\dfrac{1.75}{2.50} \times 100\%\) | \(=\) | \(70\%\) |
(i) \(\$1.75\)
(ii) \(70\%\). Check: \(0.7 \times 2.50 = 1.75\).
| \(540 - 420\) | \(=\) | \(120\) |
| \(\dfrac{120}{540} \times 100\%\) | \(=\) | \(22.22\ldots\%\) |
A loss of about \(22.2\%\). Check: \(\dfrac{120}{540} = \dfrac{2}{9}\) and \(\dfrac{2}{9} \times 540 = 120\).
(ii) A tablet is advertised at \(\$649\), including GST. Find the GST and the price before GST.
| \(1.1 \times 480\) | \(=\) | \(528\) |
| \(649 \div 11\) | \(=\) | \(59\) |
| \(649 - 59\) | \(=\) | \(590\) |
(i) \(\$528\) (the GST is \(\$48\))
(ii) \(\$59\) GST and \(\$590\) before GST. Check: \(1.1 \times 590 = 649\).
(ii) The shop sells a toaster for \(\$168\), making a profit of \(40\%\) of the cost price. Find the cost price.
| \(1.45 \times 36\) | \(=\) | \(52.2\) |
| \(168 \div 1.4\) | \(=\) | \(120\) |
(i) \(\$52.20\)
(ii) \(\$120\). Check: \(1.4 \times 120 = 168\).
(ii) A lamp sells for \(\$90\). The profit is \(20\%\) of the selling price. Find the cost price and the profit as a percentage of the cost price.
| \(1.6 \times 50\) | \(=\) | \(80\) |
| \(0.8 \times 80\) | \(=\) | \(64\) |
| \(\dfrac{14}{50} \times 100\%\) | \(=\) | \(28\%\) |
| \(0.2 \times 90\) | \(=\) | \(18\) |
| \(90 - 18\) | \(=\) | \(72\) |
| \(\dfrac{18}{72} \times 100\%\) | \(=\) | \(25\%\) |
(i) Sale price \(\$64\); profit \(\$14\), which is \(28\%\) of the cost price.
(ii) Cost price \(\$72\); the \(\$18\) profit is \(25\%\) of the cost price.
Common pitfalls
Frequently asked questions
How do you calculate percentage profit?
Divide the profit by the cost price and multiply by \(100\%\): a \(\$12\) profit on a \(\$48\) cost is \(25\%\).
How do I add GST to a price?
Multiply the price before GST by \(1.1\): \(\$250\) becomes \(\$275\).
How do I find the GST in a price that includes GST?
Divide the total by \(11\): the GST in \(\$110\) is \(\$10\).
How do I find the price before GST?
Divide the GST-inclusive total by \(1.1\): \(\$165 \div 1.1 = \$150\).
What is a mark-up?
The amount a seller adds to the cost price to make a profit, often given as a percentage of the cost price.