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Difficulty: HardProfit, Loss, and Markup

A commercial distributor purchased a shipment of 50 identical medical imaging monitors for a total cost of 20,000.Tosettheoriginallistpriceofeachmonitor,thedistributormarkedupthecostpriceperunitby75percent.Thedistributorsold30monitorsattheoriginallistprice.Tocleartheremaininginventory,thedistributorsoldtherestofthemonitorsatadiscountof20,000. To set the original list price of each monitor, the distributor marked up the cost price per unit by 75 percent. The distributor sold 30 monitors at the original list price. To clear the remaining inventory, the distributor sold the rest of the monitors at a discount of d percentofftheoriginallistprice.Ifthedistributorrealizedanoverallnetprofitof33percentontheentireshipmentof50monitors,whatisthevalueof percent off the original list price. If the distributor realized an overall net profit of 33 percent on the entire shipment of 50 monitors, what is the value of d$?

  1. A
    24
  2. B
    30
  3. C
    40
  4. 60Answer
  5. E
    84

Answer

The value of dd is 60.
The correct response accurately determines that the distributor needs 5,600fromtheremaining20monitorstoachieveanoverall33percentprofitonthe5,600 from the remaining 20 monitors to achieve an overall 33 percent profit on the 20,000 investment. This requires selling each remaining monitor for 280,whichreflectsa280, which reflects a 420 price reduction from the 700listprice.Expressedasapercentageofthe700 list price. Expressed as a percentage of the 700 list price, a $420 reduction is equal to 60 percent.

Step-by-Step Solution

1
Calculate the unit cost price and original list price per monitor
Unit cost = $20,00050=$400\frac{\$20,000}{50} = \$400. List price = $400×(1+0.75)=$700\$400 \times (1 + 0.75) = \$700.
Establishing individual unit costs and list prices is necessary to determine total revenues.
2
Determine total revenue required for an overall net profit of 33 percent
Total Target Revenue = $20,000×(1+0.33)=$26,600\$20,000 \times (1 + 0.33) = \$26,600.
An overall 33 percent profit means total revenue must equal 133 percent of the total shipment cost.
3
Calculate revenue from the first 30 monitors and the remaining required revenue
Revenue from 30 units = 30×$700=$21,00030 \times \$700 = \$21,000. Remaining revenue needed from 20 units = $26,600−$21,000=$5,600\$26,600 - \$21,000 = \$5,600.
Subtracting the revenue generated by full-price sales isolates the revenue needed from the discounted items.
4
Determine the selling price per discounted monitor and calculate the discount percentage dd
Discounted selling price = $5,60020=$280\frac{\$5,600}{20} = \$280. Discount amount = $700−$280=$420\$700 - \$280 = \$420. Discount percentage d=($420$700)×100=60d = \left(\frac{\$420}{\$700}\right) \times 100 = 60.
The discount percentage is the ratio of the dollar discount to the original list price.

Key Concept

Profit, Loss, and Markup (Successive percentage changes with mixed pricing)
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Topics

Profit, Loss, and Markup

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