smc-605-10-GST

CORE*, FUR2 2007 VCAA 3

Khan paid $900 for a fax machine.

This price includes 10% GST (goods and services tax).

Determine the price of the fax machine before GST was added. Write your answer correct to the nearest cent. (1 mark)
Khan will depreciate his $900 fax machine for taxation purposes.

He considers two methods of depreciation.

Flat rate depreciation

Under flat rate depreciation the fax machine will be valued at $300 after five years.
i. Calculate the annual depreciation in dollars. (1 mark)

Unit cost depreciation

Suppose Khan sends 250 faxes a year. The $900 fax machine is depreciated by 46 cents for each fax it sends.
ii. Determine the value of the fax machine after five years. (1 mark)

Show Answers Only

`$818.18`
1. `$120`
2. `$325`

Show Worked Solution

a. `text(Let $)P = text(price ex-GST)`

MARKER’S COMMENT: Reverse GST questions continue to cause problems for many students.

`:. P + 10text(%)P`	`= 900`
`1.1P`	`= 900`
`P`	`= 900/1.1`
	`= 818.181…`
	`= $818.18\ \ text(nearest cent)`

b.i. `text(Annual depreciation)`

`= ((900 – 300))/5`

`= $120`

b.ii. `text(Value after 5 years)`

`= 900 – (250 xx 0.46 xx 5)`

`= $325`

CORE*, FUR2 2011 VCAA 1

Tony plans to take his family on a holiday.

The total cost of $3630 includes a 10% Goods and Services Tax (GST).

Determine the amount of GST that is included in the total cost. (1 mark)

During the holiday, the family plans to visit some theme parks.

The prices of family tickets for three theme parks are shown in the table below.

What is the total cost for the family if it visits all three theme parks? (1 mark)

If Tony purchases the Movie Journey family ticket online, the cost is discounted to $202.40

Determine the percentage discount. (1 mark)

Show Answers Only

`$330`
`$462`
`text(8%)`

Show Worked Solution

a. `text(Let $)P\ text(be the cost ex-GST)`

`P + 10text(%)P`	`= 3630`
`1.1P`	`= 3630`
`P`	`= 3630/1.1`
	`= $3300`

`:.\ text(GST)`	`= 10text(%) xx $3300`
	`= $330`

b. `text(C)text(ost to visit all 3 parks)`

`= 82 + 220 + 160`

`= $462`

c.	`text(Savings)`	`= 220 – 202.40`
		`= 17.60`

`:.\ text(Discount)`	`= (17.60)/220`
	`= 0.08`
	`= 8text(%)`

CORE*, FUR2 2015 VCAA 1

Jane and Michael have started a business that provides music at parties.

The business charges customers $88 per hour.

The $88 per hour includes a 10% goods and services tax (GST).

Calculate the amount of GST included in the $88 hourly rate. (1 mark)

Jane and Michael’s first booking was a party where they provided music for four hours.

Calculate the total amount they were paid for this booking. (1 mark)

After six months of regular work, Jane and Michael decided to increase the hourly rate they charge by 12.5%.

Calculate the new hourly rate (including GST). (1 mark)

Show Answers Only

`$8`
`$352`
`$99`

Show Worked Solution

a. `text(Let)\ \ x=\ text(hourly rate before GST)`

`x +\ text(GST)`	`= 88`
`x+0.1x`	`= 88`
`x`	`=88/1.1`
	`=80`

`:.\ text(GST)\ = 88-80 = $8`

b.	`text(Total amount)`	`=88 xx 4`
		`=$352`

c.	`text(New hourly rate including GST)`
	`= 88 + 88 xx 12.5 text(%)`
	`= 88 xx 1.125`
	`=$99`

CORE*, FUR1 2010 VCAA 3 MC

Peter received a quote from the Artificial Grass Company for his new front lawn.

The quote is for $1880 plus a Goods and Services Tax (GST) of 10%.

The final amount that Peter pays for the new front lawn is

A. $188

B. $1880

C. $1890

D. $1899

E. $2068

Show Answers Only

`E`

Show Worked Solution

`text(GST)`	`= 1880 xx text(10%)`
	`= 188`

`:.\ text(Total amount)`	`= 1880 + 188`
	`= $2068`

`=> E`

CORE*, FUR1 2008 VCAA 1 MC

A plumber quoted $300, excluding GST (Goods and Services Tax), to complete a job.

A GST of 10% is added to the price.

The full price for the job will be

A. $3

B. $30

C. $303

D. $310

E. $330

Show Answers Only

`E`

Show Worked Solution

`text(GST)`	`= text(10%) xx 300`
	`= 30`

`:.\ text(Total price)`	`= 300+ 30`
	`= 330`

`=> E`

CORE*, FUR1 2006 VCAA 4 MC

An item was purchased for a price of $825.

The price included 10% GST (Goods and Services Tax).

The amount of GST included in the price is

A. $8.25

B. $75.00

C. $82.50

D. $90.75

E. $125.00

Show Answers Only

`B`

Show Worked Solution

`text(Let price without GST) = x`

♦ Mean mark 42%.
MARKERS’ COMMENT: Almost half of all students incorrectly calculated the GST as 10% of the purchase price and answered C.

`text(Price with GST)`	`= x + 10text(%) xx x`
	`= 1.1x`
`825`	`= 1.1x`
`x`	`= 750`

`:.\ text(GST)`	`= 750 xx 0.1`
	`= $75`

`=> B`

CORE*, FUR1 2011 VCAA 1 MC

An electrician charges $68 per hour to complete a job.

A Goods and Services Tax (GST) of 10% is added to the charge.

Including GST, the cost of a job that takes three hours is

A. $6.80

B. $20.40

C. $204.00

D. $210.80

E. $224.40

Show Answers Only

`E`

Show Worked Solution

`text(C) text(ost for 3 hrs)`	`= 68 xx 3`
	`= 204`

`text(GST)`	`= 204 xx 10text(%)`
	`= 20.4`

`:.\ text(Total cost)`	`= 204 + 20.4`
	`= 224.4`

`=> E`

CORE*, FUR1 2014 VCAA 4 MC

The cost of hiring a plasterer is $86.00 per hour plus GST of 10%.

The cost of hiring a plasterer for four hours, including GST, is

A. $120.40

B. $309.60

C. $344.00

D. $352.60

E. $378.40

Show Answers Only

`E`

Show Worked Solution

`text(C) text{ost per hour (incl. GST)}`

`= $86.00 + 10text(%) xx $86.00`

`= $86.00 + $8.60`

`= $94.60`

`:.\ text(C) text(ost for 4 hours)`	`=4 xx $94.60`
	`= $378.40`

`=> E`