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

When two items are sold at the same selling price ($SP$), one at a profit of $x\%$ and the other at a loss of $x\%$, there is always an overall loss given by the standard formula:

Given $x = 10$:

### Step-by-step Verification: Let the selling price of each item be $S$.

• Total Selling Price ($SP_{\text{total}}$):

  $$SP_{\text{total}} = S + S = 2S$$

• Cost Price of the first item ($CP_1$):

  $$CP_1 = \frac{S}{1 + 0.10} = \frac{S}{1.1} = \frac{10S}{11}$$

• Cost Price of the second item ($CP_2$):

  $$CP_2 = \frac{S}{1 - 0.10} = \frac{S}{0.9} = \frac{10S}{9}$$

• Total Cost Price ($CP_{\text{total}}$):

  $$CP_{\text{total}} = \frac{10S}{11} + \frac{10S}{9} = 10S \left(\frac{9 + 11}{99}\right) = \frac{200S}{99}$$

• Net Loss:

  $$\text{Loss} = CP_{\text{total}} - SP_{\text{total}} = \frac{200S}{99} - 2S = \frac{2S}{99}$$

• Loss Percentage:

  $$\text{Loss \%} = \frac{\text{Loss}}{CP_{\text{total}}} \times 100 = \frac{\frac{2S}{99}}{\frac{200S}{99}} \times 100 = \frac{2}{200} \times 100 = 1\%$$

Therefore, the transaction results in a 1% loss (Option C).