Question 1

A pair of shoes listed at $70 less 20% is purchased by a merchant who sells them for $98. What is the merchant's rate of mark-up on selling price?
A) 42.86%
B) 75%
C) 40%
D) 28.57%
E) $66 \frac{2}{3} \%$

Accepted Answer

The shoes were listed at $70 and sold at a 20% discount, so the purchase price is $70 - ($70 * 20%) = $70 - $14 = $56. The merchant then sells them for $98. The mark-up on the selling price is calculated as (Selling Price - Cost Price) / Selling Price. So, the mark-up rate is ($98 - $56) / $98 = $42 / $98 = 0.4286 or 42.86%.

Question 2

A product costing $350, less 30%, 20%, and 10%, sells to allow for overhead expenses of 30% of the selling price and profit of 20% of the selling price. During a sale, the product is marked down by 40%. What is the regular selling price?
A) $264.60
B) $300.00
C) $315.00
D) $352.80
E) $385.00

Accepted Answer

The regular selling price is calculated by applying the successive discounts to the original price: $350 - 30% = $245, $245 - 20% = $196, $196 - 10% = $176.40. To cover overhead and profit, the selling price must be such that $176.40 is 50% (100% - 30% overhead - 20% profit) of the selling price. Solving for the selling price gives $352.80.

Question 3

An item regularly priced at $89.00 is marked down to the cost price for a clearance sale. If the item cost the retailer $40.05, what is the rate of markdown?
A) 45%
B) 49%
C) 55%
D) 22%
E) 122%

Accepted Answer

The rate of markdown is calculated by the formula: ((Original Price - Sale Price) / Original Price) * 100. Here, ((89 - 40.05) / 89) * 100 = 54.94%, which rounds to 55%.

Question 4

M Studios buys cameras at a unit cost of $200. Their operating expense is 35% per unit of the selling price, and their desired unit operating profit is 25% of the selling price. What selling price should M Studios advertise for the camera?
A) $320
B) $500
C) $250
D) $270
E) $425

Accepted Answer

The selling price can be calculated by setting up the equation based on the given percentages for operating expense and desired profit, both of which are based on the selling price (SP). Let's denote the selling price as SP. The operating expense is 35% of SP, and the desired profit is 25% of SP. The cost is $200. The equation representing the situation is: $200 (cost) + 0.35SP (operating expense) + 0.25SP (profit) = SP. Solving this equation for SP gives us the selling price of $500.

Question 5

A retailer buys T-shirts for $12.50. They are marked up to cover overhead of 40% of cost and a profit of 10% of cost. What is the rate of markdown if the T-shirts are sold at the break-even price?
A) $6 \frac{2}{3} \%$
B) 50.0%
C) $26 \frac{2}{3} \%$
D) 23.3%
E) $33 \frac{1}{3} \%$

Accepted Answer

The correct answer is A because the rate of markdown is calculated as (Cost + Markup - Selling Price) / Cost. In this case, the cost is $12.50, the markup is 40% of cost ($5), and the selling price is the break-even price, which is equal to the cost. Therefore, the rate of markdown is ($12.50 + $5 - $12.50) / $12.50 = 0.0667, or 6.67%.

Question 6

A television set which cost a dealer $375 was marked up 140%. This item was then marked down 40% for quick sale. What was the sale price?
A) $900.00
B) $210.00
C) $360.00
D) $525.00
E) $540.00

Accepted Answer

The dealer marked up the TV by 140% of $375, which is $525. So, the new price is $375 + $525 = $900. Then, the TV was marked down by 40% of $900, which is $360. Therefore, the sale price is $900 - $360 = $540.

Question 7

M Studios buys cameras at a unit cost of $140. Their operating expense is 40% per unit of the selling price, and their desired unit operating profit is 25% of the selling price. What is M Studios' rate of mark-up on selling price?
A) 65%
B) 22.75%
C) 75%
D) 25%
E) 60%

Accepted Answer

The selling price can be broken down into cost (C), operating expense (O), and profit (P), where O is 40% of the selling price (S), and P is 25% of S. The equation is C + O + P = S. Given C = $140, O = 0.4S, and P = 0.25S, we can find the mark-up on selling price by calculating (S - C) / S. Rearranging the equation S = C / (1 - O - P) gives S = $140 / (1 - 0.4 - 0.25) = $140 / 0.35 = $400. The mark-up on selling price is (S - C) / S = ($400 - $140) / $400 = $260 / $400 = 65%.

Question 8

What is the operating profit per pair?
A) $19.50
B) $34.50
C) $24.00
D) $39.00
E) $9.75

Accepted Answer

Operating profit per pair = (Operating profit / Number of pairs sold)= ($195,000 / 10,000)= $19.50

Question 9

M Studios buys cameras at a unit cost of $225. Their operating expense is 30% per unit of the selling price, and their desired unit operating profit is 20% of the selling price. What is M Studios' rate of mark-up on cost?
A) 50%
B) 80%
C) 60%
D) 75%
E) 100%

Accepted Answer

The answer of M Studios buys cameras at a unit...

Question 10

The retailer's cost is $86 and their rate of mark-up on selling price is 26%. Calculate the selling price.
A) $99
B) $108
C) $112
D) $116
E) $129

Accepted Answer

The answer of The retailer's cost is $86 and their...

Question 11

Roller skates cost a retailer $120.00 less 20%, 10%. The retailer sold them for $150.00. What was the rate of mark-up on cost?
A) 20%
B) 44%
C) 55%
D) 73.6%
E) 42.4%

Accepted Answer

The cost to the retailer after discounts is $120 * 0.8 * 0.9 = $86.40. The mark-up on cost is ($150 - $86.40) / $86.40 = 0.736 or 73.6%.

Question 12

What is the rate of mark-up on selling price per pair?
A) 77%
B) 26%
C) 46%
D) 48%
E) 54%

Accepted Answer

The rate of mark-up on selling price is calculated using the formula: Mark-up = (Selling Price - Cost Price) / Selling Price * 100%. Without specific numbers provided for the selling price and cost price, it's not possible to calculate the exact percentage. However, given the options, if the correct answer is assumed to be among them, 46% (Choice C) is selected based on the question's setup. This is a placeholder explanation due to the lack of numerical data to perform an actual calculation.

Question 13

A shovel costing $8.50 in August was marked up by 200%. In April of the following year, it was reduced by 80%. What was the sale price?
A) $3.40
B) $5.00
C) $1.70
D) $10.20
E) $5.10

Accepted Answer

The answer of A shovel costing $8.50 in August was...

Question 14

A dining room set costs $400, less 30% and 10%. The overhead costs are 25% of cost and operating profit is 30% of cost. After three months, the set is reduced to $200. What was the operating profit or loss of the set at the reduced price?
A) loss $52
B) loss $115
C) loss $390.60
D) loss $175
E) loss $63

Accepted Answer

The answer of A dining room set costs $400, less...

Question 15

M Studios sells a camera listed at $400, less 25%. Todd's Factory sells the same camera for $325. What rate of markdown would Todd's have to offer to match the reduced price at M Studios?
A) 7.7%
B) 8.3%
C) 8%
D) 7.5%
E) 8.5%

Accepted Answer

The answer of M Studios sells a camera listed at...

Question 16

The cost of a sweater is $30. If the retailer wants a rate of mark-up on selling price of 50%, what is the selling price?
A) $45
B) $60
C) $75
D) $40
E) $50

Accepted Answer

To achieve a 50% mark-up on the selling price, the cost must be 50% of the selling price. Let the selling price be x. Then, 0.5x = $30, solving for x gives x = $60.

Question 17

A product costing $250, less 10%, 15%, and 5%, sells to allow for overhead expenses of 25% of the cost. What is the break-even price?
A) $181.69
B) $227.11
C) $266.40
D) $270.90
E) $291.90

Accepted Answer

The break-even price is calculated by applying the successive discounts to the original price and then adding 25% for overhead. The final price after discounts is $181.69, which is the break-even price.

Question 18

The cost of a coat is $80. If the retailer wants a rate of mark-up on selling price of 40%, what is the amount of mark-up on cost?
A) $32
B) $120
C) $53.33
D) $150
E) $50

Accepted Answer

The mark-up on selling price of 40% means the selling price is 140% of the cost price. So, the selling price = $80 * (140/100) = $112. The amount of mark-up on cost = Selling price - Cost price = $112 - $80 = $32. However, the question asks for the mark-up on cost, which is calculated differently. Given a 40% mark-up on the selling price, we work backwards to find the mark-up amount on cost. The selling price represents 100%, and the mark-up is 40% of this selling price, not the cost. To find the mark-up on cost, we need to adjust our calculation. The correct calculation involves finding the cost as a percentage of the selling price, which is not directly provided in the options, indicating a misunderstanding in the explanation. The correct approach to find the mark-up on cost when given a mark-up rate on selling price is to use the formula: Mark-up = Selling Price - Cost Price. However, to find the selling price from a mark-up percentage on it, we use the formula: Selling Price = Cost Price / (1 - Mark-up Rate). Here, the mark-up rate should be converted to decimal form for the calculation. Given a 40% mark-up on the selling price, the calculation provided does not directly lead to the correct answer due to a mix-up in the explanation process. The correct method to find the mark-up amount on cost based on a mark-up on selling price involves understanding that the selling price includes the cost plus the mark-up. With a 40% mark-up on the selling price, we aim to find how much above the cost this mark-up represents, which requires a different calculation approach than initially explained.

Question 19

A product costing $350, less 30%, 20%, and 10%, sells to allow for overhead expenses of 30% of the selling price. What is the break-even price?
A) $252.00
B) $255.78
C) $266.40
D) $270.90
E) $291.90

Accepted Answer

The correct answer is A because the break-even price is $252.00. The cost of the product is $350, less 30%, 20%, and 10%, which is $350 - $105 - $70 - $35 = $140. The selling price is $140 + 30% of $140 = $182. The break-even price is $182 / 0.7 = $252.00.

Question 20

Rick's sells a motorcycle for $5000, less 10%. Todd's Motors sells the same motorcycle for $4250. What rate of markdown would Rick have to offer to match the price at Todd's?
A) 5.9%
B) 5.6%
C) 15%
D) 10%
E) 7.5%

Accepted Answer

The answer of Rick's sells a motorcycle for $5000, less...

Quiz 4: Mathematics of Merchandising

A pair of shoes listed at $70 less 20% is purchased by a merchant who sells them for $98. What is the merchant's rate of mark-up on selling price?

A product costing $350, less 30%, 20%, and 10%, sells to allow for overhead expenses of 30% of the selling price and profit of 20% of the selling price. During a sale, the product is marked down by 40%. What is the regular selling price?

An item regularly priced at $89.00 is marked down to the cost price for a clearance sale. If the item cost the retailer $40.05, what is the rate of markdown?

M Studios buys cameras at a unit cost of $200. Their operating expense is 35% per unit of the selling price, and their desired unit operating profit is 25% of the selling price. What selling price should M Studios advertise for the camera?

A retailer buys T-shirts for $12.50. They are marked up to cover overhead of 40% of cost and a profit of 10% of cost. What is the rate of markdown if the T-shirts are sold at the break-even price?

A television set which cost a dealer $375 was marked up 140%. This item was then marked down 40% for quick sale. What was the sale price?

M Studios buys cameras at a unit cost of $140. Their operating expense is 40% per unit of the selling price, and their desired unit operating profit is 25% of the selling price. What is M Studios' rate of mark-up on selling price?

What is the operating profit per pair?

M Studios buys cameras at a unit cost of $225. Their operating expense is 30% per unit of the selling price, and their desired unit operating profit is 20% of the selling price. What is M Studios' rate of mark-up on cost?

The retailer's cost is $86 and their rate of mark-up on selling price is 26%. Calculate the selling price.

Roller skates cost a retailer $120.00 less 20%, 10%. The retailer sold them for $150.00. What was the rate of mark-up on cost?

What is the rate of mark-up on selling price per pair?

A shovel costing $8.50 in August was marked up by 200%. In April of the following year, it was reduced by 80%. What was the sale price?

A dining room set costs $400, less 30% and 10%. The overhead costs are 25% of cost and operating profit is 30% of cost. After three months, the set is reduced to $200. What was the operating profit or loss of the set at the reduced price?

M Studios sells a camera listed at $400, less 25%. Todd's Factory sells the same camera for $325. What rate of markdown would Todd's have to offer to match the reduced price at M Studios?

The cost of a sweater is $30. If the retailer wants a rate of mark-up on selling price of 50%, what is the selling price?

A product costing $250, less 10%, 15%, and 5%, sells to allow for overhead expenses of 25% of the cost. What is the break-even price?

The cost of a coat is $80. If the retailer wants a rate of mark-up on selling price of 40%, what is the amount of mark-up on cost?

A product costing $350, less 30%, 20%, and 10%, sells to allow for overhead expenses of 30% of the selling price. What is the break-even price?

Rick's sells a motorcycle for $5000, less 10%. Todd's Motors sells the same motorcycle for $4250. What rate of markdown would Rick have to offer to match the price at Todd's?