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Baguette sold 22 identical baguettes at the same price. One was sold at a 20%20\% profit and another was sold at a 20%20\% loss. Is there an overall profit or loss? Explain.

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Full solution

Q. Baguette sold 22 identical baguettes at the same price. One was sold at a 20%20\% profit and another was sold at a 20%20\% loss. Is there an overall profit or loss? Explain.
  1. Calculate Selling Price: Let the cost price of one baguette be $x\$x. The selling price of the first baguette at a 20%20\% profit is $x+0.20x=1.20x\$x + 0.20x = 1.20x.
  2. Determine Total Cost and Selling Price: The selling price of the second baguette at a 2020\% loss is $x−0.20x=0.80x\$x - 0.20x = 0.80x.
  3. Consider Profit and Loss Calculation: The total cost price for both baguettes is 2x2x, and the total selling price is 1.20x+0.80x=2x1.20x + 0.80x = 2x.
  4. Consider Profit and Loss Calculation: The total cost price for both baguettes is 2x2x, and the total selling price is 1.20x+0.80x=2x1.20x + 0.80x = 2x.Since the total selling price equals the total cost price, it seems like there is no profit or loss. However, this is a common mistake because profit and loss percentages are calculated on the cost price, not the selling price.

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