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Difficulty: MediumProfit, Loss, and Markup

An antique dealer purchased a vintage writing desk for $600\$600. To prepare the desk for sale, the dealer spent $40\$40 on restoration. The dealer then marked up the initial purchase price of $600\$600 by 50%50\% to establish the list price. During a seasonal promotion, the desk was sold at a 20%20\% discount off the list price. What was the dealer's profit as a percentage of the total expenditure (purchase price plus restoration cost)?

Answer: 12.5 %

Answer

The dealer's profit as a percentage of the total expenditure is 12.5%12.5\%.
To find the net profit percentage on total expenditure, first compute total cost ($600+$40=$640\$600 + \$40 = \$640). Next, compute list price by applying a 50%50\% markup to the initial purchase price ($600×1.50=$900\$600 \times 1.50 = \$900). Then compute the selling price after a 20%20\% discount on list price ($900×0.80=$720\$900 \times 0.80 = \$720). Net profit is selling price minus total cost ($720−$640=$80\$720 - \$640 = \$80). Finally, express net profit as a percentage of total cost: ($80/$640)×100%=12.5%(\$80 / \$640) \times 100\% = 12.5\%.

Step-by-Step Solution

1
Calculate the total cost (expenditure)
Total cost = $600+$40=$640\$600 + \$40 = \$640
The total investment includes both the purchase price of the desk and the mandatory restoration fee incurred before sale.
2
Determine the list price
List price = $600×1.50=$900\$600 \times 1.50 = \$900
The markup of 50%50\% is applied specifically to the initial purchase price of $600\$600.
3
Determine the selling price
Selling price = $900×0.80=$720\$900 \times 0.80 = \$720
The 20%20\% discount reduces the list price of $900\$900.
4
Calculate the net dollar profit
Net profit = $720−$640=$80\$720 - \$640 = \$80
Profit is calculated as total revenue (selling price) minus total cost.
5
Calculate the net profit percentage
Net profit percentage = ($80/$640)×100%=12.5%(\$80 / \$640) \times 100\% = 12.5\%
The percentage return must be evaluated using total expenditure ($640\$640) as the base.

Key Concept

Calculating successive percentage markups and discounts with secondary cost components
Estimated Time:1m 45s
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Topics

Profit, Loss, and Markup

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