Exercise: Profit, Loss & Discount
Questions for: Calculation of Selling Price, Cost Price, and Margin
A company sells a specialized tool for $320. This sale achieves a profit margin of 25% when calculated based on the selling price.
If the company maintains the same profit amount, what would be its profit margin percentage when calculated based on the cost price?
A: 25%
B: 33.33%
C: 20%
D: 75%
Answer: B
1. Calculate the profit amount from the given selling price and margin on selling price.
Profit = 25% of Selling Price = 0.25 * $320 = $80.
2. Calculate the Cost Price (CP).
Selling Price (SP) = Cost Price (CP) + Profit.
CP = SP - Profit = $320 - $80 = $240.
3. Calculate the new profit margin percentage based on the cost price.
Profit Margin % on CP = (Profit / CP) * 100.
Profit Margin % on CP = ($80 / $240) * 100.
Profit Margin % on CP = (1/3) * 100 = 33.33%.
Why others are wrong:
A — This is the initial margin calculated on the selling price, not the cost price.
C — This results from incorrectly calculating the cost price as Selling Price + Profit ($320 + $80 = $400) before determining the margin ($80/$400).
D — This represents the cost as a percentage of selling price (Cost Price / Selling Price = $240 / $320 = 0.75 or 75%), not the profit margin.
A electronics store set the list price for a new smartphone to achieve a 25% gross profit margin based on the selling price. During a promotional event, the store offered a 10% discount on the list price, selling the smartphone for $720.
What was the original cost price of the smartphone for the store?
A: $600
B: $640
C: $540
D: $620
Answer: A
1. The smartphone was sold for $720 after a 10% discount on its List Price (LP).
2. So, $720 represents 90% (100% - 10%) of the List Price.
3. Calculate the List Price: LP = $720 / 0.90 = $800.
4. The gross profit margin was 25% based on the selling price (List Price).
5. This means the Cost Price (CP) is 100% - 25% = 75% of the List Price.
6. Calculate the Cost Price: CP = 0.75 * $800 = $600.
Why others are wrong:
A — Correct calculation.
B — This results from calculating the List Price as $800 but incorrectly assuming the 25% profit margin was based on the Cost Price (CP = $800 / 1.25).
C — This results from applying the 25% margin directly to the discounted selling price of $720 (CP = $720 * 0.75).
D — This results from calculating the List Price as $800 but incorrectly subtracting 25% of the discounted selling price ($180) from it ($800 - $180).
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A furniture manufacturer produces a chair. The direct material and labor cost for each chair is $80. The manufacturer wants to achieve a 25% profit margin on the selling price. Additionally, packaging and shipping costs amount to $10 per chair.
What should be the selling price of each chair to meet the desired profit margin?
A: $120.00
B: $112.50
C: $106.67
D: $115.00
Answer: A
1. Calculate the total cost price (CP) per chair: Direct costs + Packaging/Shipping = $80 + $10 = $90.
2. Define the profit margin formula: Profit Margin = (Selling Price - Cost Price) / Selling Price.
3. We are given a desired profit margin of 25% (0.25) on the selling price (SP). So, 0.25 = (SP - $90) / SP.
4. Rearrange the formula to solve for SP: 0.25 * SP = SP - $90.
5. Subtract 0.25 * SP from both sides: $90 = SP - 0.25 * SP.
6. Simplify: $90 = 0.75 * SP.
7. Divide by 0.75: SP = $90 / 0.75.
8. Calculate the Selling Price: SP = $120.00.
Why others are wrong:
B — This calculation results from applying a 25% markup on the cost price ($90 * 1.25 = $112.50), not a 25% margin on the selling price.
C — This figure results from incorrectly ignoring the packaging and shipping costs, using only the $80 direct cost, and then calculating margin on SP ($80 / 0.75).
D — This option results from an incorrect calculation or misinterpretation of the percentage, such as adding a fixed $25 to the cost price ($90 + $25).
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A bookstore buys a novel for $15. To attract customers, they plan to offer a 20% discount on the marked price. Despite the discount, the bookstore aims to achieve a profit margin of 25% on its cost price.
What should be the marked price of the novel to meet the bookstore's objectives?
A: $21.75
B: $22.50
C: $23.44
D: $25.00
Answer: C
1. Calculate the desired profit: Profit = 25% of Cost Price ($15) = 0.25 * $15 = $3.75.
2. Calculate the Selling Price (SP): SP = Cost Price + Profit = $15 + $3.75 = $18.75.
3. The Selling Price is achieved after a 20% discount on the Marked Price (MP). This means the SP represents 80% (100% - 20%) of the MP.
4. Set up the equation: SP = 0.80 * MP => $18.75 = 0.80 * MP.
5. Solve for MP: MP = $18.75 / 0.80 = $23.4375.
6. Rounding to two decimal places, the Marked Price should be $23.44.
Why others are wrong:
A — Incorrectly adds all percentages (profit and discount) to the cost price: $15 * (1 + 0.25 + 0.20) = $21.75.
B — Incorrectly calculates the marked price by adding the discount percentage to the selling price ($18.75 * 1.20 = $22.50).
C — Correct.
D — Incorrectly calculates the profit margin as 25% of the selling price, then calculates the marked price: SP = $15 / (1 - 0.25) = $20; then MP = $20 / 0.80 = $25.00.
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A retailer purchases a new smartphone model at a cost of $450 per unit. Before selling, each unit incurs an additional $10 overhead cost for quality checks and secure packaging. The retailer aims to achieve a gross profit margin of 20% calculated on the selling price of each smartphone.
What is the minimum selling price (to the nearest cent) per smartphone the retailer must set to meet their profit margin target?
A: $575.00
B: $552.00
C: $562.50
D: $550.00
Answer: A
1. First, calculate the total cost per smartphone, which includes the purchase price and the overhead cost.
2. Total Cost = Purchase Price + Overhead Cost = $450 + $10 = $460.
3. The desired gross profit margin is 20% on the selling price (SP). This means that the total cost represents 80% (100% - 20%) of the selling price.
4. Let SP be the selling price. Then, 0.80 * SP = Total Cost.
5. 0.80 * SP = $460.
6. SP = $460 / 0.80.
7. SP = $575.00.
Why others are wrong:
B — This option incorrectly calculates a 20% markup on the total cost ($460 * 1.20 = $552.00) instead of a 20% margin on the selling price.
C — This option incorrectly calculates a 20% margin on the initial purchase price ($450 / 0.80 = $562.50), thereby ignoring the additional $10 overhead cost.
D — This option incorrectly calculates a 20% markup on the initial purchase price and then adds the overhead (($450 * 1.20) + $10 = $540 + $10 = $550.00).
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