Exercise: Profit, Loss & Discount
Questions for: Calculation of Selling Price, Cost Price, and Margin
A furniture company manufactures a desk at a total cost of $240. They intend to set the selling price to achieve a profit margin of 30% on the cost price.
What should be the selling price of the desk?
A: $312.00
B: $300.00
C: $342.86
D: $270.00
Answer: A
1. Identify the Cost Price (CP): CP = $240.
2. Identify the desired Profit Margin on Cost Price: 30%.
3. Calculate the Profit Amount: Profit = 30% of $240 = 0.30 * $240 = $72.
4. Calculate the Selling Price (SP): SP = CP + Profit = $240 + $72 = $312.00.
Why others are wrong:
B — Incorrect. This option does not correctly apply the 30% profit margin to the cost price; it represents a lower profit.
C — Incorrect. This would be the selling price if the 30% profit margin was intended to be calculated on the selling price itself, not the cost price.
D — Incorrect. This option represents a significant arithmetic error or a miscalculation of the profit amount.
A manufacturing company produces a gadget with a total production cost of $120. The company aims to achieve a profit margin of 25% on its *selling price*.
What should be the selling price of the gadget to meet this profit objective?
A: $160
B: $150
C: $96
D: $180
Answer: A
Let SP be the Selling Price and CP be the Cost Price.
Given CP = $120.
Profit margin is 25% on Selling Price, so Profit = 0.25 * SP.
The fundamental relationship is Selling Price = Cost Price + Profit.
Substitute the values: SP = CP + 0.25 * SP.
SP = $120 + 0.25 * SP.
To solve for SP, subtract 0.25 * SP from both sides of the equation:
SP - 0.25 * SP = $120.
0.75 * SP = $120.
Divide both sides by 0.75:
SP = $120 / 0.75.
SP = $160.
Why others are wrong:
A — Correct calculation.
B — This results from calculating profit as 25% of the Cost Price ($120 * 1.25 = $150), instead of the Selling Price.
C — This results from an incorrect calculation where Selling Price = Cost Price / (1 + Profit Margin) ($120 / 1.25 = $96), which would imply selling below cost and incurring a loss.
D — This represents an exaggerated selling price, possibly from an assumption of a much higher profit percentage or an incorrect multiplier application.
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A product has a base cost of $75. Packaging and shipping add an extra $15 per unit. To maintain profitability, the retailer desires a profit margin of 25% of the selling price.
What should be the selling price for one unit?
A: $120.00
B: $112.50
C: $108.00
D: $125.00
Answer: A
Step 1: Calculate the total cost price per unit.
Total Cost (TC) = Base Cost + Additional Costs = $75 + $15 = $90.
Step 2: Understand the profit margin is based on the selling price (SP).
Profit = 25% of SP = 0.25 * SP.
Step 3: Relate selling price, total cost, and profit.
SP = TC + Profit.
SP = $90 + 0.25 * SP.
Step 4: Solve for SP.
SP - 0.25 * SP = $90.
0.75 * SP = $90.
SP = $90 / 0.75.
SP = $120.00.
Why others are wrong:
A — This option correctly represents the calculated selling price based on the given profit margin on selling price.
B — This calculation incorrectly applies the 25% margin to the total cost price ($90 * 1.25 = $112.50) instead of the selling price.
C — This value likely results from a significant miscalculation of the profit margin or total cost.
D — This option represents a common miscalculation or incorrect application of the profit margin percentage.
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A furniture store purchases a sofa for $800. The store aims to achieve a profit margin of 20% on its selling price.
What should be the selling price of the sofa to achieve this desired margin?
A: $960
B: $1000
C: $1040
D: $1200
Answer: B
Let SP be the Selling Price.
Let CP be the Cost Price, which is $800.
The profit margin is 20% on the Selling Price, meaning Profit = 0.20 * SP.
We know that Selling Price (SP) - Cost Price (CP) = Profit.
Substitute the known values and the profit expression into the equation:
SP - $800 = 0.20 * SP.
Rearrange the equation to solve for SP:
SP - 0.20 * SP = $800
0.80 * SP = $800
SP = $800 / 0.80
SP = $1000.
Why others are wrong:
A — This result ($960) is obtained if the profit is incorrectly calculated as 20% of the Cost Price ($800 + 0.20 * $800).
C — This option ($1040) does not correspond to a common or logical miscalculation based on the problem's parameters.
D — This result ($1200) could arise from a multi-step error, such as first calculating profit as 20% of cost ($160), adding it to cost ($960), and then incorrectly assuming this sum represents 80% of the true selling price ($960 / 0.8).
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A bookstore aims for a gross profit margin of 25% on the selling price for all its new release hardcover books. If a particular new release hardcover book has a cost price of $36 to the bookstore,
What should be the selling price of this book to achieve the desired profit margin?
A: $45.00
B: $48.00
C: $43.20
D: $28.80
Answer: B
Let SP be the Selling Price and CP be the Cost Price.
Given CP = $36.
Gross Profit Margin = 25% on Selling Price.
This means Profit = 0.25 * SP.
We know that SP = CP + Profit.
Substitute the profit equation into the SP equation: SP = CP + 0.25 * SP.
Rearrange the equation to solve for SP:
SP - 0.25 * SP = CP
0.75 * SP = CP
SP = CP / 0.75
SP = $36 / 0.75
SP = $48.00
Why others are wrong:
A — This result ($36 * 1.25 = $45.00) would be achieved if the profit margin was 25% on the *cost price* instead of the selling price.
C — This result ($36 * 1.20 = $43.20) would be achieved if there was a 20% mark-up on the cost price, not a 25% margin on selling price.
D — This result ($36 / 1.25 = $28.80) is obtained by incorrectly dividing the cost price by (1 + profit margin), or by mistakenly applying a 25% reduction to the cost price.
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