Discussion
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
Answer: C
The person made a 1% loss.
Let each item sell for 100. The first was sold at a 10% profit, so it cost \(100/1.1 = 90.91\); the second at a 10% loss, so it cost \(100/0.9 = 111.11\).
\[ \begin{aligned} \text{cost} &= 90.91 + 111.11 = 202.02 \\ \text{loss} &= \frac{202.02 - 200}{202.02} \times 100 \approx 1\% \end{aligned} \]
The general rule: equal selling prices with equal percentage gain and loss of \(x\%\) always give a net loss of \(x^{2}/100\) percent, here \(10^{2}/100 = 1\%\). There is never a profit, which rules out both profit options, and 2% doubles the rule's result.
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