Math CentralQuandaries & Queries


Question from Mark:

If I know the amount of GST or PST collected is there a calculation to find out what the taxable amount was.
eg. 1.50 GST collected. GST is 6%. What is the taxable amount.
eg. 2.00 PST collected. PST is 8%. What is the taxable amount.

Hi Mark.

Let's say the taxable amount is the quantity A.

Then A x (0.06) = GST.
If I divide both sides of this equation by 0.06, I get:
A = GST / 0.06.

So I should be able to take the GST amount, divide by 0.06 and get the
taxable amount.

For example, if the GST was $18, then I calculate
A = $18 / 0.06
A = $300.

Does this make sense? Do the calculation the other way: what is the
GST on $300?
It is $300 x (0.06) = $18. That works.

You could use the PST calculation the same way. Assuming you are not in Quebec where the one tax is charged after the other is applied, you should get the same values:

If the GST is $1.50, then
A = $1.50 / 0.06 = $25.

If the PST is $2.00, then
A = $2.00 / 0.08 = $25.

The figures match (as they should). In Quebec it's more complicated because they must pay tax on tax.

Stephen La Rocque.

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