GST
GST (goods and services tax) adds \(10\%\) to the price of most goods and services in Australia. This NSW Year 9 Core maths subtopic revises GST from Stage 4 (NESA outcome MA4‑FRC‑C‑01), with more than half the questions working backwards from a price that already includes it.
You will add \(10\%\) GST to a price, find the GST in a GST-inclusive price by dividing by \(11\), and find the price before GST by dividing by \(1.1\), as for a \(\$594\) bill that was \(\$540\) before GST. You will also find a selling price from the GST amount alone, work out the GST a business can claim back, compare shops that quote prices with and without GST, find the GST rate in New Zealand and Singapore, and see why taking \(10\%\) off does not undo adding \(10\%\). It is part of Year 9 Core Earning Money.
Every question with a fully worked solution.
- GST - Video - How to Calculate GST Watch
Theory
GST is a \(10\%\) tax added to most goods and services in Australia. This Year 9 maths page revises the earlier work on GST and takes it further: adding GST, finding the GST inside a price, working back to the price before GST, finding a tax rate, and comparing prices.
The goods and services tax (GST) is a tax of \(10\%\) on most things sold in Australia.
The price before GST is \(100\%\). Adding \(10\%\) GST makes the price including GST \(110\%\) of it, which is \(1.1\) times as much.
A price "plus GST" does not include the tax yet. A price "including GST" already has it in.
A price including GST can be split into \(11\) equal parts: \(10\) parts are the price before GST and \(1\) part is the GST.
A registered business can claim back the GST it pays on things it buys for the business.
Adding and removing \(10\%\) GST:
| What you know | To find | Do this |
|---|---|---|
| price before GST | price including GST | \(\times 1.1\) |
| price before GST | the GST | \(\times 0.1\) |
| price including GST | price before GST | \(\div 1.1\) |
| price including GST | the GST inside it | \(\div 11\) |
| the GST | price including GST | \(\times 11\) |
How to solve a GST problem
- Read whether the price given includes GST or not.
- Choose the move: \(\times 1.1\) to add GST, \(\div 1.1\) to remove it, \(\div 11\) for the GST inside a price.
- Work out the answer and round money to the nearest cent.
- Check: the price before GST plus the GST should equal the price including GST.
(i) A desk is priced at $240 before GST. Find the GST and the price including GST.
(ii) An invoice lists parts at $150 and labour at $310, both before GST. Find the total including GST.
(i) The GST is \(10\%\) of the price. The price paid is \(110\%\) of it.
| \(\text{GST}\) | \(=\) | \(0.1 \times 240 = \mathbf{24.00}\) |
| \(\text{price}\) | \(=\) | \(1.1 \times 240 = \mathbf{264.00}\) |
(ii) Add the items first, then add the GST to the total.
| \(\text{before GST}\) | \(=\) | \(150 + 310 = 460\) |
| \(\text{GST}\) | \(=\) | \(0.1 \times 460 = 46\) |
| \(\text{total}\) | \(=\) | \(460 + 46 = \mathbf{506.00}\) |
The desk costs $264.00 and the invoice total is $506.00.
(i) A bill is $594, including \(10\%\) GST. Find the GST and the price before GST.
(ii) A ticket costs $9.95 including GST. Find the price before GST, to the nearest cent.
(i) Divide by \(11\) for the GST. Divide by \(1.1\) for the price before GST.
| \(\text{GST}\) | \(=\) | \(594 \div 11 = \mathbf{54.00}\) |
| \(\text{before GST}\) | \(=\) | \(594 \div 1.1 = \mathbf{540.00}\) |
Check: \(540 + 54 = 594\) \(\checkmark\)
(ii)
| \(\text{before GST}\) | \(=\) | \(9.95 \div 1.1\) |
| \(\) | \(=\) | \(9.0454\ldots\) |
| \(\) | \(\approx\) | \(\mathbf{9.05}\) |
The GST in (ii) is $9.95 − $9.05 = $0.90.
(i) The GST included in the price of a pair of shoes is $6.40. Find the price before GST and the selling price.
(ii) In another country, a meal costs $80 before tax and $86 after tax. What is the rate of tax?
(i) The GST is one part in eleven, so the price before GST is \(10\) parts and the selling price is \(11\) parts.
| \(\text{before GST}\) | \(=\) | \(10 \times 6.40 = \mathbf{64.00}\) |
| \(\text{selling price}\) | \(=\) | \(11 \times 6.40 = \mathbf{70.40}\) |
(ii) Write the increase as a percentage of the price before tax.
| \(\text{increase}\) | \(=\) | \(86 - 80 = 6\) |
| \(\text{rate}\) | \(=\) | \(\dfrac{6}{80} \times 100\%\) |
| \(\) | \(=\) | \(\mathbf{7.5\%}\) |
(i) A $60 item has \(10\%\) GST added. Show that taking \(10\%\) off the new price does not give $60.
(ii) Shop A sells a heater for $132 including GST. Shop B sells it for $121 plus GST. Which is cheaper, and by how much?
(i)
| \(1.1 \times 60\) | \(=\) | \(66.00\) |
| \(0.9 \times 66\) | \(=\) | \(59.40\) |
The second \(10\%\) is of \(66\), not \(60\), so it is too big. The correct way back is \(66 \div 1.1 = 60\).
(ii) Put both prices on the same basis: including GST.
| \(\text{Shop B}\) | \(=\) | \(1.1 \times 121 = 133.10\) |
| \(\text{difference}\) | \(=\) | \(133.10 - 132 = \mathbf{1.10}\) |
Shop A is cheaper by $1.10.
Common pitfalls
Frequently asked questions
How do you add GST to a price?
Multiply the price before GST by \(1.1\). For a price of $240, the price including GST is $264.
How do you work out the GST in a price that includes GST?
Divide the price by \(11\). A bill of $594 including GST has $54 of GST in it.
How do you remove GST from a price?
Divide the price including GST by \(1.1\). A price of $594 including GST was $540 before GST.
Why do you divide by 11 to find GST?
With \(10\%\) GST, the price is \(110\%\) of the price before tax. That is \(11\) equal parts of \(10\%\) each, and only one of them is the tax.
Why doesn't taking 10 percent off undo adding 10 percent GST?
Because the \(10\%\) taken off is of the bigger price. Adding \(10\%\) to $60 gives $66, but \(10\%\) off $66 gives $59.40.