Question

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of:

• A. ( 1% , {profit} )
• B. ( 2% , {profit} )
• C. ( 1% , {loss} )
• D. ( 2% , {loss} )

Hint:

For questions involving equal selling prices with both profit and loss, use the formula: [ {Overall loss percentage} = frac{({Profit percentage} times {Loss percentage})}{100}. ] This simplifies calculations without requiring assumptions.

Answer 1

The Correct Option is C

Step 1: Understanding the problem.

The person sells two items at the same selling price. For one item, he makes a \( 10\% \) profit, and for the other, he incurs a \( 10\% \) loss. We need to calculate the overall gain or loss percentage.

Step 2: Assume selling price and calculate cost prices.

Let the selling price of each item be \( 100 \) units.

• For the first item with \( 10\% \) profit:

\[ \text{Cost price of the first item} = \frac{\text{Selling price}}{1 + \frac{\text{Profit percentage}}{100}} = \frac{100}{1.1} = 90.91 \text{ units.} \]

• For the second item with \( 10\% \) loss:

\[ \text{Cost price of the second item} = \frac{\text{Selling price}}{1 - \frac{\text{Loss percentage}}{100}} = \frac{100}{0.9} = 111.11 \text{ units.} \] Step 3: Calculate total cost price and total selling price.

• Total cost price:

\[ \text{Total cost price} = 90.91 + 111.11 = 202.02 \text{ units.} \]

• Total selling price:

\[ \text{Total selling price} = 100 + 100 = 200 \text{ units.} \] Step 4: Calculate overall loss percentage.

The overall loss is:

\[ \text{Loss} = \text{Total cost price} - \text{Total selling price} = 202.02 - 200 = 2.02 \text{ units.} \]

The loss percentage is:

\[ \text{Loss percentage} = \frac{\text{Loss}}{\text{Total cost price}} \times 100 = \frac{2.02}{202.02} \times 100 \approx 1\%. \] Conclusion.

The overall result is a \( 1\% \) loss. Thus, the correct answer is:

Correct Answer: (C) \( 1\% \) loss.