smc-1125-20-GST

v1 Financial Maths, STD1 F1 2021 HSC 12

A karate school runs a holiday program and charges $150 per student.

The costs of running the program are:

Karate instructor: $110 per hour

Hall hire: $52 per hour plus 10% GST.

The program runs for two hours a day for five days.

What profit does the karate school make if 20 students pay for the program? (3 marks)

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`$1328`

Show Worked Solution

`text(Revenue) = 20 xx 150 = $3000`

`text(Cost per hour)`	`= 110+(52 xx 1.1)`
	`= 110+57.20`
	`= $167.20`

`text(Total cost)`	`= 2 xx 5 xx 167.20`
	`= $1672`

`:.\ text(Profit)`	`= 3000-1672`
	`= $1328`

v1 Financial Maths, STD2 F1 2007 HSC 6 MC

The price of a book is $33.00, which includes 10% GST.

What is the amount of GST included in this price?

$2.75
$3.00
$3.50
$30.00

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`B`

Show Worked Solution

`text(Book costs $33.00 incl. GST)`

`text(Let)\ C = text(original cost)`

`C + 10\% × C`	`= 33`
`1.1C`	`= 33`
`C`	`= 30`

`:.\text(GST)`	`= 33.00-30.00`
	`= $3.00`

`=> B`

Financial Maths, STD1 F1 2024 HSC 4 MC

The cost of a plumbing job is $500 plus 10% GST.

What is the total cost of the job, including GST?

$45
$50
$545
$550

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$D$

Show Worked Solution

$\text{Total Cost}$	$=500+0.10\times 500$
	$=500+50$
	$=$550$

$\Rightarrow D$

Financial Maths, STD1 F1 2023 HSC 7 MC

An item was purchased for a price of $$880$, including $10\%$ GST.

What is the amount of GST included in the price?

$$8.00$
$$8.80$
$$80.00$
$$88.00$

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$C$

Show Worked Solution

$\text{Let}\ C =\text{Original cost}$

$C+0.1 \times C$	$=880$
$1.1C$	$=880$
$C$	$=\dfrac{880}{1.1}$
	$=$800$

$\therefore \text{GST}=800\times 0.1=$80$

$\Rightarrow C$

♦ Mean mark 15%.

Financial Maths, STD1 F1 2021 HSC 12

A dance school runs a holiday program and charges $150 per student.

The costs of running the program are:

Dance teacher: $110 per hour

Room hire: $52 per hour plus 10% GST.

The program goes for two hours a day for five days.

What profit does the dance school make if 20 students pay for the program? (3 marks)

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`$1328`

Show Worked Solution

`text(Revenue) = 20 xx 150 = $3000`

`text(C)text(ost per hour)`	`= 110 + (52 + \text{GST})`
	`= 110 + 52 xx 1.1`
	`= $167.20`

`text(Total cost)`	`= 2 xx 5 xx 167.20`
	`= $1672`

`:.\ text(Profit)`	`= 3000 – 1672`
	`= $1328`

Financial Maths, STD1 F1 2019 HSC 29

Part of a supermarket receipt is shown.

Determine the missing values, `A` and `B`, to complete the receipt. (2 marks)

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`$9.00`

Show Worked Solution

`text(Chocolate is the only item where GST applies.)`

`text(GST on chocolate = 0.70)`

`=> text(C)text(ost of chocolate) = $7.00`

`:. A = 7.00 + 0.70 = $7.70`

`:. B`	`= 36.25 – (7.70 + 5.00 + 8.50 + 3.20 + 2.85)`
	`= $9.00`

Financial Maths, STD2 F1 SM-Bank 5

Alex is buying a used car which has a sale price of $13 380. In addition to the sale price there are the following costs:

Stamp Duty for this car is calculated at $3 for every $100, or part thereof, of the sale price.
Calculate the Stamp Duty payable. (1 mark)

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Alex wishes to take out comprehensive insurance for the car for 12 months.

The cost of comprehensive insurance is calculated using the following:

Find the total amount that Alex will need to pay for comprehensive insurance. (3 marks)

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Alex has decided he will take out the comprehensive car insurance rather than the less expensive non-compulsory third-party car insurance.
What extra cover is provided by the comprehensive car insurance? (1 mark)

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`$402`
`$985.74`
`text(Comprehensive insurance covers Alex)`
`text(for damage done to his own car as well.)`

Show Worked Solution

♦♦♦ Mean mark 12%
IMPORTANT: “or part thereof ..” in the question requires students to round up to 134 to get the right multiple of $3 for their calculation.

i.	`($13\ 380)/100 = 133.8`

`:.\ text(Stamp duty)`	`= 134 xx $3`
	`= $402`

ii.

`text(Base rate) = $845`

`text(FSL) =\ text(1%) xx 845 = $8.45`

`text(Stamp)`	`=\ text(5.5%) xx(845 + 8.45)`
	`= 46.9397…`
	`= $46.94\ text{(nearest cent)}`

`text(GST)`	`= 10 text(%) xx(845 + 8.45)`
	`= 85.345`
	`= $85.35`

`:.\ text(Total cost)`	`= 845 + 8.45 + 46.94 + 85.35`
	`= $985.74`

♦ Mean mark 34%.

iii.	`text(Comprehensive insurance covers Alex)`
	`text(for damage done to his own car as well.)`

Financial Maths, STD2 F1 2015 HSC 15 MC

A camera costs $449, including 12% GST.

What is the price of the camera without GST, correct to the nearest dollar?

`$395`
`$401`
`$437`
`$503`

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`B`

Show Worked Solution

`text(Let)\ C\ text(= cost of camera ex-GST)`

♦ Mean mark 36%.

`C + text(12%)C`	`= $449`
`1.12C`	`= 449`
`:. C`	`= 449/1.12`
	`= $400.89…`

`⇒ B`

Financial Maths, STD2 F1 2004 HSC 17 MC

Rita purchased a camera for $880 while on holidays in Australia. This price included 10% GST. When she left Australia she received a refund of the GST.

What was Rita’s refund?

$80
$88
$792
$800

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`A`

Show Worked Solution

`text(Let)\ C = text(cost before GST)`

`880`	`= C + text(10%) C`
`1.1C`	`= 880`
`C`	`= $800`

`:.\ text(GST)`	`=10 text(%) xx 800`
	`= $80`

`=> A`

Financial Maths, STD2 F1 2007 HSC 6 MC

The price of a CD is $22.00, which includes 10% GST.

What is the amount of GST included in this price?

$2.00
$2.20
$19.80
$20.00

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`A`

Show Worked Solution

`text(CD costs $22.00 incl. GST`

`text(Let)\ C = text(original cost)`

`C + text(10%) xx C`	`= 22`
`1.1C`	`= 22`
`C`	`= 20`

`:.\ text(GST)`	`= 22.00 – 20.00`
	`= $2.00`

`=> A`

Financial Maths, STD2 F1 2010 HSC 2 MC

A new phone was purchase for $725 which included 10% GST.

What was the price of the phone without GST, correct to the nearest cent?

$65.91
$72.50
$652.50
$659.09

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`D`

Show Worked Solution

♦ Mean mark 44%.
COMMENT: A surprise this was so poorly answered. Ensure you understand this tax!

`text(Price phone)\ +\ text(10% GST)`	`=725`
`text(110%)\ xx\ text(Phone price)`	`=725`
`:.\ text(Phone price)`	`=725/1.1`
	`=$659.09`

`=> D`

\(\text{Total Cost}\)	\(=500+0.10\times 500\)
	\(=500+50\)
	\(=$550\)

\(C+0.1 \times C\)	\(=880\)
\(1.1C\)	\(=880\)
\(C\)	\(=\dfrac{880}{1.1}\)
	\(=$800\)