smc-831-30-% Increase/Decrease

v1 Financial Maths, STD2 F1 2007 HSC 3 MC

Dan is about to go on holidays for four weeks. His weekly salary is $375 and his holiday loading is 20% of four weeks pay.

What is Dan's total pay for the four weeks holiday?

$400
$1250
$1800
$2150

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`C`

Show Worked Solution

`text(Salary)\ text{(4 weeks)}`	`= 4 xx 375`
	`= $1500`

`text(Holiday loading)`	`= 1500 xx 20%`
	`= $300`

`:.\ text(Total pay)`	`= 1500+300`
	`= $1800`

`=> C`

v1 Financial Maths, STD2 F1 SM-Bank 7

A laptop was on sale with a 30% discount.

As a student, Max received a further 15% off the already discounted price.

What was the overall percentage discount Max received? (2 marks)

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`text(40.5%)`

Show Worked Solution

`text{Solution 1 (efficient method)}`

`text(Overall discount)`	`= 1-(0.70 xx 0.85)`
	`= 1-0.595`
	`= 0.405`
	`= 40.5text(%)`

`text(Solution 2)`

`text(Let the laptop cost) = $100`

`text(Cost after 30% discount) = $70`

`text(Cost after another 15% discount)`

`= 70-(0.15 xx 70)`

`= $59.50`

`:.\ text(Overall discount) = 100-59.50=40.5text(%)`

v1 Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases the cost price by 25%. In a sale, the retail price is reduced by 25% to give the sale price.

How does the sale price compare to the cost price?

The sale price is less than the cost price.
The sale price is the same as the cost price.
The sale price is more than the cost price.
It is impossible to compare without knowing the cost price.

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`text(A)`

Show Worked Solution

`text{Assume the item costs $100:}`

`=>\ \text{Retail price} = 100 × 1.25 = $125`

`=>\ \text{Sale price} = 125 × 0.75 = $93.75`

`:.\ \text{Sale price < Cost price}`

`=>\ \text{A}`

Financial Maths, STD2 F1 2023 HSC 13 MC

An item is discounted by 30% and then a further discount of 20% is applied to the reduced price.

What is the total percentage discount?

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`=>B`

Show Worked Solution

`text{Method 1}`

`text{Let original price}\ =x`

`text{1st discount}\ =0.7x`

`text{2nd discount}\ = 0.7x xx 0.8=0.56x`

`text{Total discount}\ = 1-0.56=0.44`

♦♦ Mean mark 47%.

`text{Method 2}`

`text{$100 less 30% = $70}`

`text{$70 less 20%} = 70-0.2xx70=$56`

`text{Total discount $100 ↓ $56 = 44%}`

`=>B`

Financial Maths, STD2 F1 2019 HSC 7 MC

Julia earns $28 per hour. Her hourly pay rate increases by 2%.

How much will she earn for a 4-hour shift with this increase?

$2.24
$28.56
$112
$114.24

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`D`

Show Worked Solution

`text(Hourly rate)`	`= 28 xx 1.02`
	`= $28.56`

`:.\ text(Shift earnings)`	`= 4 xx 28.56`
	`= $114.24`

`=> D`

Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases its cost price by 30%. In a sale, the retails price is reduced by 30% to give the sale price.

How does the sale price compare to the cost price?

The sale price is less than the cost price.
The sale price is the same as the cost price.
The sale price is more than the cost price.
It is impossible to compare without knowing the cost price.

Show Answers Only

`text(A)`

Show Worked Solution

`text{Take an item that costs $100 (for example):}`

♦ Mean mark 50%.

`=>\ text(Original price) = 100 xx 1.3 = $130`

`=>\ text(Sale Price) = 130 xx 0.7 = $91`

`:.\ text(Sale price < cost price)`

`=>\ text(A)`

Financial Maths, STD2 F1 SM-Bank 7

A dress was on sale with 25% discount.

As a regular customer, Kate received a further 10% on the already discounted price.

What was the overall percentage discount Kate received? (2 marks)

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`text(32.5%)`

Show Worked Solution

`text{Solution 1 (efficient method)}`

`text(Overall discount)`	`=1-(0.75 xx 0.90)`
	`=1-0.675`
	`=0.325`
	`=32.5text(%)`

`text(Solution 2)`

`text(Let the dress cost) = $100`

`text(C) text(ost after 25% discount) = $75`

`text(C) text(ost after another 10% discount)`

`= 75 – (10 text{%} xx 75)`

`= $67.50`

`:.\ text(Overall discount) = 32.5text(%)`

Financial Maths, STD2 F1 SM-Bank 12

A golf shop is having a Boxing Day sale.

What is the percentage discount on a putter which is reduced from $120.00 to $102.00? (1 mark)

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The same discount applies storewide. What discount amount is applicable to a box of golf balls whose original price was $25.00? (1 mark)

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What is the sale price of a golf bag which originally cost $160.00 (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

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`15 text(%)`
`$3.75`
`$136.00`

Show Worked Solution

i.	`text(Percentage Discount)`	`=(120-102)/120 xx 100`
		`=18/120 xx 100`
		`=15 text(%)`

ii.	`text(Discounted Amount)`	`=15 text(%) xx 25`
		`=$3.75`

iii.	`text(Sale Price)`	`= 160 – 15 text(%) xx 160`
		`=0.85 xx 160`
		`=$136.00`

Financial Maths, STD2 F1 2015 HSC 25 MC

An insurance company offers customers the following discounts on the basic annual premium for car insurance.

If a customer is eligible for more than one discount, subsequent discounts are applied to the already discounted premium. The combined compulsory third party (CTP) and comprehensive insurance discount is always applied last.

Jamie has three insurance policies, including combined CTP and comprehensive insurance, with this company. He has used this company for 8 years and he has never made a claim.

The basic annual premium for his car insurance is $870.

How much will Jamie need to pay after the discounts are applied?

$482.44
$515.50
$541.60
$557.60

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`C`

Show Worked Solution

`text(Multi-policy discount)`

`text(New premium)`	`= 870 − (text(15%) xx 870)`
	`= $739.50`

`text(No claim bonus)`

`text(New premium)`	`= 739.50 − (text(20%) xx 739.50)`
	`= $591.60`

`text(Combined CTP bonus)`

`text(New premium)`	`= 591.60 − 50`
	`= $541.60`

`⇒ C`

Financial Maths, STD2 F1 2007 HSC 3 MC

Joe is about to go on holidays for four weeks. His weekly salary is $280 and his holiday loading is 17.5% of four weeks pay.

What is Joe’s total pay for the four weeks holiday?

$196
$329
$1169
$1316

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`D`

Show Worked Solution

`text(Salary)\ text{(4 weeks)}`	`= 4 xx 280`
	`= $1120`

`text(Holiday loading)`	`= 1120 xx 17.5%`
	`= $196`

`:.\ text(Total pay)`	`= 1120 + 196`
	`= $1316`

`=> D`

Financial Maths, STD2 F1 2014 HSC 18 MC

The average NSW annual water consumption from the residential sector is equal to 90 340 litres per person per year. The Building Sustainability Index (BASIX) uses this as the benchmark to set a target for reducing water consumption by up to 40%.

A new building, planned to house 50 people, has been designed to meet a 25% reduction on this water consumption benchmark.

How much water per year, to the nearest kilolitre, is this building designed to save when fully occupied?

1129
1807
2710
3388

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`A`

Show Worked Solution

`text(Benchmark) = 90\ 340\ text(L)`

`text(Water saved if usage)\ darr text(25%)`

`= 90\ 340 xx text(25%)`

`= 22\ 585\ text(L per person)`

`:.\ text(Water saved for 50 people)`

`= 50 xx 22\ 585`

`= 1\ 129\ 250\ text(L)`

`~~ 1129\ text(kL)`

`=> A`

Financial Maths, STD2 F1 2010 HSC 23a

This advertisement appeared in a newspaper

What is the maximum possible salary per annum for this civil engineer, correct to the nearest dollar? (2 marks)

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`$86\ 396`

Show Worked Solution

`text(Base wage)=1586.70\ text(pw)`

`text(Max weekly base)`	`=$1586.70+(text{3.5%}\ xx 1586.70)`
	`=1586.70+55.53`
	`=1642.23\ text((nearest cent))`

`:.\ text(Max annual base)`	`=1642.23xx52`
	`=85\ 395.96`
	`=$85\ 396\ text{(nearest dollar)}`