The ratio of the cost price of two articles X and Y is \(1:2\). A businessman earns a profit of \(p\%\) by selling X and a loss of \(3p\%\) by selling Y. If he loses \(20\%\) in this transaction, then what is the value of \(p\)?
12%
Let the cost price of X be \(k\) and of Y be \(2k\), so total cost price \(=3k\). Profit on X \(=\frac{pk}{100}\) and loss on Y \(=\frac{3p(2k)}{100}=\frac{6pk}{100}\). Net loss \(=\frac{6pk}{100}-\frac{pk}{100}=\frac{5pk}{100}\). This equals \(20\%\) of \(3k\), i.e. \(\frac{5pk}{100}=\frac{20}{100}\times 3k\), giving \(5p=60\), so \(p=12\).
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