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Question
If the cost price of 18 chairs be equal to selling price of 16 chairs, find the gain or loss percent.
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Solution
\[\text { Let the cost price of one chair be Rs . C, and selling price be Rs } . S \]
\[\text { Therefore, }18C = 16S\]
\[C = \frac{16}{18}S\]
\[\text { As cost price is less than the selling price }, \]
\[S . P . = \left( \frac{100 +\text { profit % }}{100} \right)C . P\]
\[S = \left( \frac{100 + \text { profit % }}{100} \right)C\]
\[\frac{S}{C} = \left( \frac{100 + \text { profit % }}{100} \right)\]
\[\frac{18}{16} = \left( \frac{100 +\text { profit % }}{100} \right)\]
\[\frac{1800}{16} = 100 + \text { profit %} \]
\[\frac{1800}{16} - 100 = \text { profit % } \]
\[\text { Profit % } = \frac{1800 - 1600}{16}\]
\[ = \frac{200}{16}\]
\[ = 12 . 5\]
\[\text { Therefore, the required profit percent is 12 . 5 % }. \]
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