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If a trader sells two articles at the same price, one at a loss of x% and the other at a profit of y%, then the trader makes approximately what profit or loss. How to got about solving this??

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If the two selling prices are each $p$ and the costs were $c_1$ and $c_2$ then $$p = c_1\left(1-\frac{x}{100}\right)$$ and $$p = c_2\left(1+\frac{y}{100}\right)$$ so you can calculate the overall percentage profit (or loss if negative) from $$\left(\frac{2p}{c_1+c_2}-1\right)\times 100. $$

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