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Difficulty: MediumProfit and Loss

A rare book dealer recorded the financial details for four different inventory items. Match each item's transaction history to its final profit or loss percentage.

  • First edition novel: purchased for $120\$120 and sold for $150\$15025%25\% Profit
  • Antique atlas: purchased for $300\$300, plus $100\$100 for restoration, and sold for $320\$32020%20\% Loss
  • Signed biography: purchased for $60\$60 and sold for $90\$9050%50\% Profit
  • Vintage encyclopedias: purchased for $80\$80 and sold for $72\$7210%10\% Loss

Answer

The transactions match their respective percentages by dividing the net dollar profit or loss by the total initial cost.
Each correct pair accurately reflects the percentage change from the initial total investment. The total cost always serves as the base (denominator) for these percentage calculations.

Step-by-Step Solution

1
Calculate the profit percentage for the first edition novel.
Profit is $150−$120=$30\$150 - \$120 = \$30. Percentage is 30120=25%\frac{30}{120} = 25\%.
To find the profit percentage, divide the absolute profit by the original purchase cost.
2
Calculate the total cost and loss percentage for the antique atlas.
Total cost is $300+$100=$400\$300 + \$100 = \$400. Loss is $400−$320=$80\$400 - \$320 = \$80. Percentage is 80400=20%\frac{80}{400} = 20\%.
Overhead and restoration costs must be added to the purchase price to determine the true initial cost.
3
Calculate the profit percentage for the signed biography.
Profit is $90−$60=$30\$90 - \$60 = \$30. Percentage is 3060=50%\frac{30}{60} = 50\%.
Dividing the absolute profit by the initial cost provides the correct percentage.
4
Calculate the loss percentage for the vintage encyclopedias.
Loss is $80−$72=$8\$80 - \$72 = \$8. Percentage is 880=10%\frac{8}{80} = 10\%.
Dividing the dollar loss by the original cost yields the correct loss percentage.

Key Concept

Calculating profit and loss percentages by dividing the net financial change by the total initial cost, ensuring all overhead is included.
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Topics

Profit and Loss

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