Discounts and mark-ups | Year 8

01 / LEARN

The idea, step by step

Keep the price stages separate

A shop may buy an item at a cost price, add a mark-up to choose a listed price, and later offer a discount. Each percentage is taken from a stated base. A mark-up on cost uses the cost as 100%; a discount normally uses the listed price as 100%.

Use a short price chain: cost â†’ listed price â†’ sale price. Calculate one stage at a time, keeping the amounts labelled. Profit in dollars is the actual selling price minus the cost; a discount is not automatically a loss.

Compare profit and percentage language

A 25% mark-up means the listed price is 125% of cost. If a later discount is 20%, multiply this listed price by 0.8. You cannot subtract the two percentage rates to obtain the overall change, because their whole amounts differ.

When asked for profit as a percentage of cost, divide profit by cost and multiply by 100%. If the question instead uses selling price as the base, the percentage will differ. Always state which base you used.

A common trap

A 40% mark-up followed by a 20% discount gives a 20% profit.

Instead: The combined multiplier is $1.4 \times 0.8 = 1.12$ , giving a 12% profit on cost.

02 / WORKED EXAMPLES

See the thinking

Example 1

Mark up a cost

A shop buys a lamp for 40 AUD and adds a 25% mark-up. Find the listed price.

The multiplier is $1.25$ .
$40 \times 1.25 = 50$ .
The mark-up is 10 AUD, one quarter of 40 AUD.

50 AUD

Example 2

A sale can still make a profit

An item costs a shop 50 AUD. It is marked up by 40%, then discounted by 20%. Find the sale price and profit.

Listed price: $50 \times 1.4 = 70$ AUD.
Sale price: $70 \times 0.8 = 56$ AUD.
Profit: $56 - 50 = 6$ AUD; as a percentage of cost, $6 \div 50 \times 100 % = 12 %$ .

Sale price 56 AUD; profit 6 AUD, or 12% of cost.

Check your understanding

An item costing 60 AUD is marked up by 20%. Find the listed price.

Show answer

72 AUD

$60 \times 1.2 = 72$ .

03 / WORKSHEET

Your turn

6 questions · 16 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Mark up a 30 AUD cost by 20%.
2 marks
Discount a listed price of 90 AUD by 10%.
2 marks
An item costs 48 AUD and is sold for 60 AUD. Find its dollar profit and percentage profit on cost.
3 marks
A listed price of 80 AUD is reduced by 15%. Find the sale price.
2 marks
An item costs 80 AUD. It is marked up by 25%, then discounted by 10%. Find its final price and profit on cost.
4 marks
A store buys a book for 24 AUD and lists it at 30 AUD. What is the greatest percentage discount on the listed price that avoids selling below cost?
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Mark up a 30 AUD cost by 20%.
2 marks
$30 \times 1.2 = 36$ .
36 AUD
Discount a listed price of 90 AUD by 10%.
2 marks
$90 \times 0.9 = 81$ .
81 AUD
An item costs 48 AUD and is sold for 60 AUD. Find its dollar profit and percentage profit on cost.
3 marks
Profit: $60 - 48 = 12$ AUD.
$12 \div 48 \times 100 % = 25 %$ .
12 AUD; 25%
A listed price of 80 AUD is reduced by 15%. Find the sale price.
2 marks
$80 \times 0.85 = 68$ .
68 AUD
An item costs 80 AUD. It is marked up by 25%, then discounted by 10%. Find its final price and profit on cost.
4 marks
$80 \times 1.25 = 100$ .
$100 \times 0.9 = 90$ .
$90 - 80 = 10$ , and $10 \div 80 \times 100 % = 12.5 %$ .
90 AUD; 10 AUD profit or 12.5%
A store buys a book for 24 AUD and lists it at 30 AUD. What is the greatest percentage discount on the listed price that avoids selling below cost?
3 marks
The store may reduce the price by $30 - 24 = 6$ AUD.
$6 \div 30 \times 100 % = 20 %$ .
At 20% off, the sale price is exactly 24 AUD.
20%

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Percentage increase/decrease; finding an original amount; discounts and mark-ups; percentage comparisons; budgets and purchase decisions; modelling and checking financial problems with digital tools. Simple interest can be offered here as a school-dependent application and developed in Year 9.

Official curriculum source ↗

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