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:

When equal selling prices are given, the overall result depends on the cost price difference and the percentage profit or loss for each item.

Answer 1

The Correct Option is C

Let the selling price (SP) of each item be $100 \, \text{units}$. Step 1: Calculate the cost price (CP) for each item. For the first item, there is a $10\%$ profit: $$\text{CP}_1 = \frac{\text{SP}_1}{1.1} = \frac{100}{1.1} \approx 90.91 \, \text{units}.$$ For the second item, there is a $10\%$ loss: $$\text{CP}_2 = \frac{\text{SP}_2}{0.9} = \frac{100}{0.9} \approx 111.11 \, \text{units}.$$ Step 2: Compute the total cost price and total selling price. $$\text{Total CP} = \text{CP}_1 + \text{CP}_2 = 90.91 + 111.11 = 202.02 \, \text{units}.$$ $$\text{Total SP} = 100 + 100 = 200 \, \text{units}.$$ Step 3: Determine the overall profit or loss. $$\text{Loss} = \text{Total CP} - \text{Total SP} = 202.02 - 200 = 2.02 \, \text{units}.$$ $$\text{Loss percentage} = \frac{\text{Loss}}{\text{Total CP}} \times 100 = \frac{2.02}{202.02} \times 100 \approx 1\%.$$ Final Answer: $$\boxed{\text{1\% loss}}$$