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Difficulty: HardProfit, Loss, and Markup

An antique dealer purchased three items—an armchair, a desk, and a cabinet—for a total combined cost of $4,000\$4,000. The cost of the desk was 20%20\% greater than the cost of the armchair, and the cost of the cabinet was 50%50\% greater than the cost of the desk. To determine the list price for each item, the dealer marked up the cost of the armchair by 40%40\%, the cost of the desk by 50%50\%, and the cost of the cabinet by 30%30\%. During a clearance event, the dealer sold the armchair at a 15%15\% discount off its list price, the desk at a 20%20\% discount off its list price, and the cabinet at its full list price with no discount. What was the dealer's overall profit as a percentage of the total combined purchase cost of the three items?

  1. A
    23.00%23.00\%
  2. 24.25%24.25\%Answer
  3. C
    28.75%28.75\%
  4. D
    19.52%19.52\%
  5. E
    38.00%38.00\%

Answer

The dealer's overall profit was 24.25%24.25\% of the total combined purchase cost.
The correct response of 24.25%24.25\% accurately calculates the individual item costs, applies sequential markup and discount multipliers (1.40×0.85=1.191.40 \times 0.85 = 1.19 for armchair, 1.50×0.80=1.201.50 \times 0.80 = 1.20 for desk, 1.301.30 for cabinet), sums the final sales revenue to $4,970\$4,970, and evaluates net profit ($970\$970) over total cost ($4,000\$4,000).

Step-by-Step Solution

1
Determine the individual cost of each item
Armchair cost = $1,000\$1,000, Desk cost = $1,200\$1,200, Cabinet cost = $1,800\$1,800
Let AA be the cost of the armchair. The desk cost is 1.2A1.2A, and the cabinet cost is 1.5×1.2A=1.8A1.5 \times 1.2A = 1.8A. The total cost is A+1.2A+1.8A=4.0A=4,000  ⟹  A=1,000A + 1.2A + 1.8A = 4.0A = 4,000 \implies A = 1,000.
2
Calculate the list price and selling price for each item
Armchair selling price = $1,190\$1,190; Desk selling price = $1,440\$1,440; Cabinet selling price = $2,340\$2,340
Armchair list price = $1,000×1.40=$1,400\$1,000 \times 1.40 = \$1,400; selling price = $1,400×0.85=$1,190\$1,400 \times 0.85 = \$1,190. Desk list price = $1,200×1.50=$1,800\$1,200 \times 1.50 = \$1,800; selling price = $1,800×0.80=$1,440\$1,800 \times 0.80 = \$1,440. Cabinet selling price = list price = $1,800×1.30=$2,340\$1,800 \times 1.30 = \$2,340.
3
Find total revenue and total profit
Total revenue = $4,970\$4,970, Total profit = $970\$970
Total revenue = $1,190+$1,440+$2,340=$4,970\$1,190 + \$1,440 + \$2,340 = \$4,970. Total profit = $4,970−$4,000=$970\$4,970 - \$4,000 = \$970.
4
Compute overall profit percentage on total cost
24.25%24.25\%
Overall profit percentage = (9704000)×100%=24.25%(\frac{970}{4000}) \times 100\% = 24.25\%.

Key Concept

Successive Percentage Changes and Weighted Profit Base Calculations
Estimated Time:2m 0s
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Topics

Profit, Loss, and Markup

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