171
6.1 Markup and Markdown
Markup
Markup is the amount that a business adds to the cost of a product to arrive at the selling price of
that product.
Cost + Markup = Selling Price
Markup
Therefore, Markup = Selling Price – Cost
The amount of markup includes: 1. the business overhead expenses,
such as rent, utilities, insurance, advertising, etc., that are necessary to
operate the business, and 2. the desired operating profit of the business.
Markup is usually expressed as a percent of cost, known as the rate of
markup.
Markup = Rate of Markup × Cost
Markup
Markup
Markup
n×100%
Therefore, Rate
Rate
Rate
ofofMarkup
ofMarkup
Markup
==e=
×100%
×100%
Cost
Cost
Cost
Example 6.1-a
Selling Price
Cost
Exhibit 6.1-a Relationship among
Markup, Cost, and
Selling Price
Calculating Selling Price and Rate of Markup
A store purchases printers for $800 each. If the markup on each printer is $600, calculate:
Solution
(i)
The selling price
(ii)
The rate of markup
(i)
Selling Price = Cost + Markup
= 800.00 + 600.00
= $1,400.00
Markup = $600
Rate of Markup = ?
Selling Price = ?
Cost = $800
Therefore, the selling price of each printer is $1,400.00.
(ii)
 Markup 
Rate of Markup = 
 ×100%
 Cost 
600.00 
= 
 × 100%
 800.00 
= 75.00%
Therefore, the rate of markup is 75.00%.
Example 6.1-b
Calculating Cost and Rate of Markup
A retailer sells a handbag for $87.75. If the markup on each handbag is $22.75, calculate:
Solution
(i)
The cost of each handbag
(ii)
The rate of markup on each handbag
(i)
Cost + Markup = Selling Price
Cost = Selling Price – Markup
= 87.75 – 22.75
Markup = $22.75
Rate of Markup = ?
Selling Price = $87.75
Cost = ?
= $65.00
Therefore, the cost of each handbag is $65.00.
6.1 Markup and Markdown
172
Solution
continued
(ii)
 Markup 
Rate of Markup = 
 ×100%
 Cost 
 22.75 
=
 × 100%
 65.00 
= 35.00%
Therefore, the rate of markup is 35.00%.
Example 6.1-c
Calculating Markup and Rate of Markup
A wholesaler purchases cell phones for $65.60 each and sells them for $82.00 each. Calculate:
Solution
(i)
The amount of markup on each cell phone
(ii)
The rate of markup
(i)
Markup = Selling Price – Cost
Markup = ?
Rate of Markup = ?
= 82.00 – 65.60
= $16.40
Selling Price = $82.00
Cost = $65.60
Therefore, the amount of markup on each cell phone is $16.40.
(ii)
 Markup 
Rate of Markup = 
 ×100%
 Cost 
 16.40 
=
 × 100%
 65.60 
= 25.00%
Therefore, the rate of markup on each cell phone is 25.00%.
Example 6.1-d
Calculating Markup and Selling Price
A wholesaler purchases a product for $2,000. If he has a markup of 40% on the cost of the product,
calculate:
Solution
(i)
The amount of markup
(ii)
The selling price of the product
(i)
Markup = Rate of Markup × Cost
= 0.40 × 2,000.00
= $800.00
Therefore, the amount of markup is $800.00.
(ii)
Selling Price = Cost + Markup
= 2,000.00 + 800.00
= $2,800.00
Therefore, the selling price is $2,800.00.
Chapter 6 | Applications of Ratios and Percents
Markup = ?
Rate of Markup = 40%
Cost = $2,000
Selling Price = ?
173
Example 6.1-e
Calculating Cost and Selling Price
A car dealership sells used cars with a 20% markup on cost. The amount of markup on a used car sold
was $2,950. Calculate:
Solution
(i)
The cost of the car to the dealer
(ii)
The selling price
(i)
Markup = $2,950
Rate of Markup = 20%
 Markup 
Rate of Markup = 
 ×100%
 Cost 
Markup
n # 100 %
Cost = d
Rate of Markup
Selling Price = ?
Cost = ?
 2, 950.00 
=
 × 100%
 20% 
= $14,750.00
Therefore, the cost of the car is $14,750.00.
(ii)
Selling Price = Cost + Markup
= 14,750.00 + 2,950.00
= $17,700.00
Therefore, the selling price is $17,700.00.
Markdown
The Selling Price of an item
refers to the regular (or
normal) selling price; i.e.,
the price before Markdown.
Markdown is the amount by which the selling price of a product is reduced in determining the sale
price.
Selling Price – Markdown = Sale Price
Markdown
Therefore, Markdown = Selling Price – Sale Price
In business, the selling price of an item is often reduced for various reasons,
such as competition, clearance of seasonal items, etc.
The Sale Price of an item
refers to the reduced (or
discounted) selling price. i.e.,
the price after Markdown.
Example 6.1-f
Markdown is usually expressed as a percent of the selling price, known as
the rate of markdown.
Markdown = Rate of Markdown × Selling Price
 Markdown 
Therefore, Rate of Markdown = 
 ×100%
 Selling Price 
Selling Price
Sale Price
Exhibit 6.1-b Relationship
among Selling
Price, Markdown,
and Sale Price
Calculating Sale Price (Reduced Selling Price) and Rate of Markdown
Calculate the sale price and rate of markdown of an item that regularly sells for $680, but is now being
marked down by $204.
Solution
Selling Price − Markdown = Sale Price
Sale Price = Selling Price − Markdown
Markdown = $204.00
Rate of Markdown = ?
= 680.00 − 204.00
= $476.00
Therefore, the sale price of the item is $476.00.
Selling Price = $680.00
Sale Price = ?
6.1 Markup and Markdown
174
Solution
continued
 Markdown 
 ×100%
Rate of Markdown = 
 Selling Price 
 204.00 
=
 × 100%
 680.00 
= 30.00%
Therefore, the rate of markdown is 30.00%.
Example 6.1-g
Calculating Markdown and Sale Price (Reduced Selling Price)
An item was marked down by 20% from the regular selling price of $1,250. Calculate:
Solution
(i)
The amount of markdown
(ii)
The sale price
(i)
Markdown = Rate of Markdown × Selling Price
= 0.20 × 1,250.00
= $250.00
Markdown = ?
Rate of Markdown = 20%
Selling Price = $1,250.00
Sale Price = ?
Therefore, the amount of markdown was $250.00.
(ii)
Sale Price = Selling Price − Markdown
= 1,250.00 − 250.00
= $1,000.00
Therefore, the sale price was $1,000.00.
Example 6.1-h
Calculating the Selling Price and Rate of Markdown
After a markdown of $276.50, an item was sold for $513.50. Calculate:
Solution
(i)
The regular selling price
(ii)
The rate of markdown
(i)
Selling Price = Sale Price + Markdown
= 513.50 + 276.50
= $790.00
Markdown = $276.50
Rate of Markdown = ?
Selling Price = ?
Therefore, the regular selling price was $790.00.
(ii)


Rate of Markdown =  Markdown  ×100%
 Selling Price 
 276.50 
=
 × 100%
 790.00 
= 0.35 × 100% = 35.00%
Therefore, the rate of markdown was 35.00%.
Example 6.1-i
Calculating Markdown and Rate of Markdown
During a sale, a shirt that was regularly priced at $49.00, sold for $41.65. Calculate:
(i)
The amount of markdown
(ii)
Rate of markdown
Chapter 6 | Applications of Ratios and Percents
Sale Price = $513.50
175
Solution
(i)
Sale Price = Selling Price − Markdown
Markdown = ?
Rate of Markdown = ?
Markdown = Selling Price − Sale Price
= 49.00 − 41.65
Selling Price = $49.00
Sale Price = $41.65
= $7.35
Therefore, the markdown was $7.35.
(ii)
 Markdown 
 ×100%
Rate of Markdown = 
 Selling Price 
 7.35 
=
 × 100%
 49.00 
= 0.15 × 100%
= 15.00%
Therefore, the rate of markdown was 15.00%.
Calculating Selling Price and Sale Price (Reduced Selling Price)
Example 6.1-j
During a sale, an item was marked down by $150 after a markdown of 20%. Calculate,
Solution
(i)
The regular selling price
(ii)
The sale price
(i)
Markdown = $150.00
Rate of Markdown = 20%
Markdown = Rate of Markdown × Selling Price
Markdown
Selling Price =
Rate of Markdown
150.00
=
0.20
Selling Price = ?
Sale Price = ?
= $750.00
Therefore, the regular selling price was $750.00.
(ii)
Sale Price = Selling Price – Markdown
= 750.00 – 150.00
= $600.00
Therefore, the sale price was $600.00.
6.1 Exercises
Answers to odd-numbered problems are available at the end of the textbook.
For the following problems, express the answers rounded to two decimal places, wherever applicable.
Calculate the missing values in Problems 1 to 10:
Cost ($)
Markup ($)
Selling Price ($)
Rate of Markup (%)
1.
$99.00
$24.75
?
?
2.
$37.50
$15.00
?
?
3.
?
$52.50
$490.00
?
4.
?
$67.50
$517.50
?
5.
$52.00
?
$97.50
?
6.
$50.40
?
$63.00
?
7.
$252.00
?
?
35.00%
6.1 Markup and Markdown
176
Cost ($)
Markup ($)
Selling Price ($)
Rate of Markup (%)
8.
$210.00
?
?
90.00%
9.
?
$175.00
?
12.50%
10.
?
$62.90
?
40.00%
11. A store sells a camera that costs $270 for $430. Find the amount of markup and the rate of markup.
12. A bicycle costs a store $64.50. If the store sells the bicycle for $93.15, calculate the amount of markup and the rate of
markup.
13. A furniture shop purchased a certain mattress for $625, and marked it up by $325. Calculate the selling price and the
rate of markup.
14. A store purchases monitors for $86.25 each. The store’s markup is $31.50. Calculate the selling price and the rate of
markup.
15. A computer store used a markup rate of 40%. Find the amount of markup and the selling price of a computer software
DVD that the store bought for $38.75.
16. I purchased a laptop for $187.50 for the purpose of reselling it later. If my rate of markup is 90% of the cost, what is
the amount of markup and the selling price?
17. The selling price of an item is $540. If the markup is $108, calculate the cost and rate of markup of the item.
18. A DVD player is sold for $124 after a markup of $27. Calculate the cost and rate of markup of the DVD player.
19. A bookstore uses a 40% markup on calculators and the amount of markup of a particular calculator was $24. Calculate
the bookstore’s purchase price of the calculator and its selling price.
20. If a $96 markup of an item represents an 80% rate of markup on cost, calculate the cost and the selling price of that
item.
21. An item that cost $1,800 to a store is marked up by 35% of the cost. Calculate the amount of markup and the selling
price.
22. The cost of school bags to a store is $19 each. The store marked it up by 20% of the cost. Calculate the amount of
markup and the selling price.
23. A bookstore sells a finance math textbook for $142.80. The cost of the book to the store is $105.00. Calculate the
amount of markup and the rate of markup on cost.
24. The cost of an item to a store is $80 and its retail selling price is $130. Calculate the amount of markup and the rate
of markup on cost.
25. The amount of markup of an item is $7.50 and the rate of markup on cost is 15%. Calculate the cost and the selling
price of the item.
26. A store sells each refrigerator at a markup of $224.70. If the rate of markup on cost is 30%, calculate the cost and the
selling price of each refrigerator.
Calculate the missing values in Problems 27 to 36:
Selling Price ($)
Markdown ($)
Sale Price ($)
Rate of Markdown (%)
27.
$94.75
$74.50
?
?
28.
$90.40
$22.60
?
?
29.
$136.00
?
?
22.50%
30.
$72.90
?
?
40.00%
31.
?
$34.00
$46.00
?
32.
?
$36.75
$173.25
?
33.
$25.00
?
$17.50
?
34.
$58.50
?
$29.25
?
35.
?
$31.71
?
25.00%
36.
?
$150.00
?
37.50%
Chapter 6 | Applications of Ratios and Percents
177
37. During a sale, a sofa that regularly sells for $250 is marked down by $75. Calculate the sale price and the rate of
markdown.
38. A scanner that regularly sells for $99 was sold after a markdown of $29. Calculate the sale price and the rate of
markdown.
39. A treadmill with a regular selling price of $190 is on sale for 15% off the original price. Calculate the amount of
markdown and the sale price.
40. The regular selling price of a rocking chair is $139. During a sale, it was sold after a markdown of 25%. Find the
amount of markdown and the sale price.
41. A store offers an $18 discount on a bookcase and it was sold for $30. Calculate the regular selling price of the bookcase
and the rate of discount offered.
42. Calculate the regular selling price and the rate of markdown of an item sold for $27.30 after a markdown of $18.20
during a sale.
43. A fax machine that regularly sells for $127.50 is marked down to $86.70 during a special sale. Find the percent
markdown and the amount of markdown during the sale.
44. A camcorder regularly selling for $299.00 was marked down to sell for $233.22. Find the percent markdown and the
amount of markdown.
45. During a sale, a furniture store marked down all the items by 35%. The amount of markdown on a bed was $166.25.
Find the regular selling price and the sale price.
46. A winter jacket was sold after a markdown of $16.25. If this represents a markdown rate of 13%, find the regular
selling price and the sale price of the winter jacket.
47. A TV that regularly sells for $699.00 was sold for $615.12. Calculate the amount of markdown and the rate of markdown.
48. During a sale, Mythili bought a piano for $4,532.50. If the regular selling price was $4,900.00, calculate the amount
of markdown and the rate of markdown.
49. Girija bought a dress for $22 after a markdown of 12%. Calculate the regular selling price and the amount of
markdown.
50. Aran bought a video game for $31.96 after a markdown of 15%. Calculate the regular selling price and the amount
of markdown.
51. A toaster that regularly sells for $37.50 was sold after a markdown of $3.75. Calculate the sale price and the rate of
markdown.
52. A football was sold after a markdown of $19.25. If the original price was $55.00, calculate the sale price and the rate
of markdown.
53. During a sale, a humidifier was sold for $279.65 after a markdown of 15%. Calculate the regular selling price and the
amount of markdown.
54. After a markdown of 12.5%, a bicycle was sold for $112. Calculate the regular selling price and the amount of
markdown.
6.2 Simple Interest
Calculations Involving Simple Interest
Interest is a fee that borrowers pay to lenders for using their money temporarily for a period of time.
For example, when we invest money, the financial institution uses our money and therefore, pays us
interest for the time period it has been invested. Similarly, when we borrow money from a financial
institution, we pay interest to them for the time period borrowed.
In simple interest calculations, Interest (I) is calculated as a percent (%) of the initial amount of
money invested or borrowed, known as the Principal (P). Therefore,
Interest = Principal × Interest Percent
Interest = Principal × Interest Rate × Time
I=P×r×t
6.2 Simple Interest