Ten markup and markdown problems with full solutions, written the way they appear on
business math homework and exams. Each one lists what is given and what to find, then
works every step. They cover markup on cost and on selling price, finding the cost or
selling price, converting between the two bases, markdown percent, successive
markdowns, and breakeven and lowest acceptable prices.
Rounding: interim values stay exact; money is rounded to the nearest cent at the end.
Example 1 · Basic
Find the markup and both markup percents
A garden center buys a ceramic planter for $48 and sells it for $72. Find the markup in dollars, the markup as a percent of cost, and the markup as a percent of the selling price.
Cost
$48.00
Selling price
$72.00
Find
Markup, markup on cost and markup on selling price
Solution
Write the formulas
Markup = Selling price − Cost
Markup on cost = Markup ÷ Cost
Markup on selling price = Markup ÷ Selling price
Find the markup
$72.00 − $48.00 = $24.00
Find the markup percent on cost
$24.00 ÷ $48.00 = 0.5
0.5 × 100 = 50%
Find the markup percent on selling price
$24.00 ÷ $72.00 ≈ 0.333333 (rounded to six decimal places)
Answer: The cost is the other 70% of the selling price, so Selling price = $84.00 ÷ 0.7 = $120.00 and the markup is $36.00. Taking 30% of the cost instead would give only a $109.20 price.
A supplier quotes a markup of 60% on cost. What is that as a percent of the selling price? Then convert a markup of 40% of the selling price to a percent of cost.
First markup
60% of cost
Second markup
40% of selling price
Find
The converted markup percent
Solution
60% of cost to selling price
Write the formula
Markup on selling price = Markup on cost ÷ (1 + Markup on cost)
Markup on cost = Markup on selling price ÷ (1 − Markup on selling price)
Subtract the markup on selling price from 100%
40% = 0.4
100% − 40% = 60% = 0.6
Divide the markup rate by that number
0.4 ÷ 0.6 ≈ 0.666667 (rounded to six decimal places)
Change the decimal to a percent
0.666667 × 100 = 66.6667%
Check with a $100 example
Cost $60.00, selling price $100.00, markup $40.00
$40.00 ÷ $100.00 = 40% of selling price
$40.00 ÷ $60.00 ≈ 66.6667% of cost
Answer: On cost 60% is 0.6 ÷ 1.6 = 37.5% of the selling price. A 40% markup on selling price is 0.4 ÷ 0.6 ≈ 66.6667% of cost. A markup on selling price is always the smaller number.
A $200 coat is marked down 20%, and a month later the sale price is marked down another 10%. Find the final price, and compare it with a single 30% markdown.
Original price
$200.00
Markdowns
20% then 10%
Find
Final price
Solution
Successive markdowns
Write the formulas
Each markdown is taken from the price left by the one before it.
Net factor = (1 − m₁) × (1 − m₂) × …
Final price = Original selling price × Net factor
Subtract each markdown rate from 100%
100% − 20% = 80% = 0.8
100% − 10% = 90% = 0.9
Multiply the complements
0.8 × 0.9 = 0.72
Find the final price
$200.00 × 0.72 = $144.00
Find the single equivalent markdown
100% − 72% = 28%
Total markdown: $200.00 − $144.00 = $56.00
A single 30% markdown
Write the formulas
Markdown = Original selling price × Markdown rate
Sale price = Original selling price − Markdown
Change the percent to a decimal
30% = 30 ÷ 100 = 0.3
Find the markdown
$200.00 × 0.3 = $60.00
Subtract the markdown from the original price
$200.00 − $60.00 = $140.00
The shopper pays $4.00 more after 20% and 10% than after a flat 30%.
Answer: Net factor = 0.8 × 0.9 = 0.72, so the final price is $200.00 × 0.72 = $144.00. The single equivalent markdown is 28%, not 30%. A single 30% markdown would leave $140.00.
A furniture store buys a side table for $46. Operating expenses are $14 per table and the original selling price is $80. Find the breakeven price and the largest markdown the store can take. Then find the lowest acceptable price and the largest markdown if the store still wants an $8 profit.
Cost
$46.00
Operating expenses
$14.00
Original price
$80.00
Desired profit (second part)
$8.00
Find
Lowest acceptable price and maximum markdown
Solution
No profit required
Write the formulas
Breakeven price = Cost + Operating expenses
Maximum markdown = Original selling price − Lowest acceptable price
Maximum markdown percent = Maximum markdown ÷ Original selling price
Maximum markdown = Original selling price − Lowest acceptable price
Maximum markdown percent = Maximum markdown ÷ Original selling price
Find the breakeven price
$46.00 + $14.00 = $60.00
Add the desired profit
$60.00 + $8.00 = $68.00
Find the maximum markdown
$80.00 − $68.00 = $12.00
Find the maximum markdown percent
$12.00 ÷ $80.00 = 0.15
0.15 × 100 = 15%
Answer: Breakeven price = $46.00 + $14.00 = $60.00, so the largest markdown is $80.00 − $60.00 = $20.00, which is 25% of the original price. With the $8.00 profit the lowest acceptable price is $68.00 and the largest markdown is $12.00, or 15%.
Problems and businesses on this page are original practice problems written for
Business Math Lab. Answers are checked by automated tests against the solver.