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A customer buys two items for $120 each. If the first item has a profit of 20% a

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Question: A customer buys two items for $120 each. If the first item has a profit of 20% and the second has a loss of 20%, what is the overall profit or loss? (2023)

Options:

  1. No profit, no loss
  2. Loss of $12
  3. Profit of $12
  4. Profit of $24

Correct Answer: No profit, no loss

Exam Year: 2023

Solution: 

Cost Price of first item = 100, Selling Price = 120. Cost Price of second item = 150, Selling Price = 120. Total Cost Price = 250, Total Selling Price = 240. Overall loss = 10.

A customer buys two items for $120 each. If the first item has a profit of 20% a

Practice Questions

Q1
A customer buys two items for $120 each. If the first item has a profit of 20% and the second has a loss of 20%, what is the overall profit or loss? (2023)
  1. No profit, no loss
  2. Loss of $12
  3. Profit of $12
  4. Profit of $24

Questions & Step-by-Step Solutions

A customer buys two items for $120 each. If the first item has a profit of 20% and the second has a loss of 20%, what is the overall profit or loss? (2023)
  • Step 1: Identify the selling price of each item. Both items are sold for $120 each.
  • Step 2: Calculate the cost price of the first item. Since it has a profit of 20%, we can use the formula: Selling Price = Cost Price + (Profit Percentage * Cost Price).
  • Step 3: Let the cost price of the first item be 'x'. The equation becomes: 120 = x + (0.20 * x).
  • Step 4: Simplify the equation: 120 = x + 0.2x, which is 120 = 1.2x.
  • Step 5: Solve for 'x': x = 120 / 1.2 = 100. So, the cost price of the first item is $100.
  • Step 6: Calculate the cost price of the second item. It has a loss of 20%, so we use the formula: Selling Price = Cost Price - (Loss Percentage * Cost Price).
  • Step 7: Let the cost price of the second item be 'y'. The equation becomes: 120 = y - (0.20 * y).
  • Step 8: Simplify the equation: 120 = y - 0.2y, which is 120 = 0.8y.
  • Step 9: Solve for 'y': y = 120 / 0.8 = 150. So, the cost price of the second item is $150.
  • Step 10: Calculate the total cost price of both items: Total Cost Price = Cost Price of first item + Cost Price of second item = 100 + 150 = 250.
  • Step 11: Calculate the total selling price of both items: Total Selling Price = Selling Price of first item + Selling Price of second item = 120 + 120 = 240.
  • Step 12: Determine the overall profit or loss: Overall Profit/Loss = Total Selling Price - Total Cost Price = 240 - 250 = -10.
  • Step 13: Since the result is negative, it indicates an overall loss of $10.
  • Profit and Loss Calculation – Understanding how to calculate profit and loss based on cost price and selling price.
  • Percentage Calculations – Applying percentage changes to determine profit or loss on individual items.
  • Total Cost and Selling Price – Summing up the total cost and selling prices to find overall profit or loss.
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