Markup and Markdown

Learn how stores set prices with a markup on the cost price and lower them with a markdown, and how to find the percent, the original price and the result of stacked discounts.

Intermediate25 min18 problems
Practice Problems

Definition

A store buys an item at its cost price and sells it at a higher selling price. The extra amount is the markup. Later the store may lower the price: that reduction is a markdown (also called a discount), and the new price is the sale price.
Both use a multiplier:
Selling price=Cost×(1+p)\text{Selling price} = \text{Cost} \times (1 + p)
Sale price=Original price×(1−d)\text{Sale price} = \text{Original price} \times (1 - d)
Here pp is the markup rate and dd is the discount rate, written as decimals (25% = 0.250.25).
Which price is the base?
  • A markup percent is always a percent of the cost price.
  • A markdown percent is always a percent of the original price (the price before the sale).
Two changes in a row multiply: 20% off and then 10% off gives 0.80×0.90=0.720.80 \times 0.90 = 0.72, so you pay 72% and save 28%, not 30%.

Try it now

A store marks up an item that cost 50 dollars by 20%. Which calculation gives the selling price?

Worked Examples

A sports shop buys a backpack for 40 dollars and adds a 35% markup. What is the selling price?
1

Find the markup amount (a percent of the cost)

40×0.35=1440 \times 0.35 = 14 dollars → Markup = 14 dollars
2

Add it to the cost price

40+14=5440 + 14 = 54 dollars
3

Check with the multiplier

40×1.35=5440 \times 1.35 = 54 → Same answer

Common Mistakes

Adding two discounts: 20% off and then 10% off = 30% off

Why it's wrong: The second discount is taken from the already reduced price, which is smaller than the original price, so it saves less.

Correct: Multiply the multipliers: 0.80×0.90=0.720.80 \times 0.90 = 0.72. You pay 72%, so the total discount is 28%.

Finding the original price by adding the percent to the sale price (63+30%63 + 30\% of 63=81.9063 = 81.90)

Why it's wrong: The 30% was a percent of the original price, not of the sale price. Using the sale price as the base gives a number that is too small.

Correct: Divide by the multiplier: 63÷0.70=9063 \div 0.70 = 90. Check: 90×0.70=6390 \times 0.70 = 63.

Dividing the markup by the selling price (90340≈26%\frac{90}{340} \approx 26\%)

Why it's wrong: A markup percent is measured against the cost price, the price the store paid.

Correct: Markup percent =markupcost×100%= \frac{\text{markup}}{\text{cost}} \times 100\%, here 90250=36%\frac{90}{250} = 36\%.

Thinking a 25% markdown undoes a 25% markup

Why it's wrong: The markdown is taken from the larger selling price, so it removes more than the markup added: 80×1.25=10080 \times 1.25 = 100, then 100×0.75=75100 \times 0.75 = 75.

Correct: The price ends 5 below the cost of 80. To get back from 100 to 80 you need a 20% markdown: 100×0.80=80100 \times 0.80 = 80.

Interactive Visual

Ratio Tape Diagram

Cost price (100%)
20
20
20
20
= 80
Markup (25%)
20
= 20
Selling price (125%)
= 5 (100)
If total is:
Cost price (100%) value:80
Markup (25%) value:20

Ratio Tape Diagram

Sale price (70%)
6
6
6
6
6
6
6
= 42
Discount (30%)
6
6
6
= 18
Original price (100%)
= 10 (60)
If total is:
Sale price (70%) value:42
Discount (30%) value:18

Bar Chart

20% off, then 10% off is not 30% off

Original(200 dollars)
−20%(160 dollars)
Then −10%(144 dollars)
Once −30%(140 dollars)

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

18 problems
Problem 1 of 18
Easy
A store marks up an item that cost 50 dollars by 20%. Which calculation gives the selling price?

Why It Matters

In the lesson Percent Increase and Decrease you learned the multipliers 1+p1 + p and 1−d1 - d. Markup and markdown are where those multipliers meet real money:
  • Shops add a markup to cover rent, staff and profit before an item reaches the shelf.
  • Sales like 40% off are markdowns from the original price.
  • Stacked coupons (an extra 15% off at the checkout) are successive discounts, and they always save less than the two percents added together.
  • Price tags often show only the sale price, so finding the original price is a useful check.
  • Small businesses need to know whether a sale price is still above the cost price.
With these skills you can check any price tag and see which deal really is better.

Real World Applications

Clothing Store Pricing

Fashion shops often mark up new items a lot and mark them down at the end of the season. The question is whether the sale price still covers the cost.

Example:

A shirt bought for 20 dollars with a 100% markup sells for 20×2=4020 \times 2 = 40 dollars. Half price later is 20 dollars: no profit at all.

1Try It Yourself

A store buys a dress for 60 dollars and marks it up 50%. At the end of the season the dress is marked down 30%.

What is the final sale price in dollars?

Step 1: Write the mathematical expression

Apply the markup, then the markdown:

Stacked Coupons on Sale Days

On big sale days shops often offer a discount plus an extra coupon at the checkout. The coupon is taken from the already reduced price.

Example:

50% off and then an extra 50% off is not free: 0.5×0.5=0.250.5 \times 0.5 = 0.25, so you still pay 25% of the price.

2Try It Yourself

A TV costs 500 dollars. It is 20% off, and a coupon takes an extra 15% off the reduced price.

What is the total discount in percent? (Enter the number only.)

Step 1: Write the mathematical expression

Compare the final price with the original price:

Reading a Sale Tag

Outlet stores often show only the sale price and the discount. Working backwards tells you the original price and how much you really save.

Example:

A tag says 25% off, now 30 dollars. The original price was 30÷0.75=4030 \div 0.75 = 40 dollars.

3Try It Yourself

A pair of sneakers has a tag: 40% off, now 48 dollars.

What was the original price in dollars?

Step 1: Write the mathematical expression

Divide the sale price by the multiplier:

Key Takeaways

  • 1Selling price = cost price × (1 + markup rate); the markup percent is a percent of the cost price
  • 2Sale price = original price × (1 - discount rate); the markdown percent is a percent of the original price
  • 3Percent of markup = markup ÷ cost × 100%; percent of markdown = discount ÷ original price × 100%
  • 4To find the original price from a sale price, divide by the multiplier (63 ÷ 0.70 = 90), never add the percent back
  • 5Successive discounts multiply: 20% then 10% off is 0.80 × 0.90 = 0.72, a 28% discount, not 30%
  • 6A markup followed by a markdown of the same percent ends below the start: 1.25 × 0.75 = 0.9375

Frequently Asked Questions

No. Markup is a percent of the cost price, margin is a percent of the selling price. An item bought for 80 and sold for 100 has a 25% markup (20 of 80) but a 20% margin (20 of 100).
No. Markup is a percent of the cost price, margin is a percent of the selling price. An item bought for 80 and sold for 100 has a 25% markup (20 of 80) but a 20% margin (20 of 100).
Yes. A 100% markup doubles the cost price, and a 200% markup makes the selling price three times the cost. Some shops use markups this large on cheap items.
No. A 100% markdown already makes the price 0. A store cannot take off more than the whole price.
No. Multiplication can be done in any order: 0.80×0.90=0.90×0.80=0.720.80 \times 0.90 = 0.90 \times 0.80 = 0.72. 20% then 10% off gives the same price as 10% then 20% off.

Glossary

Cost price
The price a store pays for an item
Selling price
The price a store asks from customers: cost price plus markup
Markup
The amount (or percent of the cost price) a store adds to the cost price
Markdown (discount)
The amount (or percent of the original price) taken off a price
Sale price
The price after a markdown
Multiplier
The number you multiply by to apply a percent change, such as 1.35 for a 35% markup or 0.60 for 40% off

Formula Card

Selling price

Selling price=Cost×(1+p)\text{Selling price} = \text{Cost} \times (1 + p)

Apply a markup of rate p to the cost price

Sale price

Sale price=Original×(1−d)\text{Sale price} = \text{Original} \times (1 - d)

Apply a markdown of rate d to the original price

Percent of markup

Selling price−CostCost×100%\frac{\text{Selling price} - \text{Cost}}{\text{Cost}} \times 100\%

The base is the cost price

Percent of markdown

Original−Sale priceOriginal×100%\frac{\text{Original} - \text{Sale price}}{\text{Original}} \times 100\%

The base is the original price

Original price

Original=Sale price1−d\text{Original} = \frac{\text{Sale price}}{1 - d}

Work backwards from a sale price

Today's challengeOne problem, three tries

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