Find the GST and the pre-GST price from an inclusive price

The whole receipt is taxable at 10%. How much of the GST-inclusive $60.50 is tax?

Someone removes 10% of a $275 inclusive price, then adds 10% to the remainder. Will the rebuilt amount equal $275?

Try different divisors to guess the tax. Subtract that guess, then add 10% to the remainder. Find the divisor that rebuilds the actual total, and check another price. Displayed amounts are rounded to cents

For every position of the price slider, for which divisor did adding 10% GST back rebuild the price you started with?

The inclusive total has eleven parts

For a fully taxable purchase at 10%, the inclusive total is 110% of its before-tax price. Ten parts are the original price and one part is tax

1. 1Recognise the 110% The inclusive amount is 100% of the original price plus 10% GST, so it is 110% of the original \(\displaystyle 100\% + 10\% = 110\% = \frac{11}{10}\)
2. 2Divide by eleven for GST The GST is one of the 11 equal parts in the inclusive price \(\displaystyle \$60.50 \div 11 = \$5.50\)
3. 3Subtract GST for the original price Remove the tax from the inclusive total to recover the price before GST \(\displaystyle \$60.50 - \$5.50 = \$55\)
4. 4Use the equivalent multiplier Dividing by 1.1 gives the same pre-GST price as subtracting the GST after dividing by 11 \(\displaystyle \$60.50 \div 1.1 = \$55\)

Total including GST

\(\displaystyle \$319\)

The entire receipt is taxable at 10%. Find the GST component

Identify the tax share of the inclusive total

Price including GST

\(\displaystyle \$148.50\)

GST rate

\(\displaystyle 10\%\)

Recover the price before GST for this fully taxable item

Reverse the multiplier that turns a before-tax price into the inclusive price

Store A, including GST

\(\displaystyle \$242\)

Store B, excluding GST

\(\displaystyle \$210\)

Compare the final prices a customer pays. Both offers are fully taxable at 10%. How much cheaper is Store B?

Put both offers on an inclusive basis before subtracting

A student removes GST from $220 by subtracting $22, giving $198. Which forward check exposes the mistake?