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Question
If the selling price of 18 oranges is equal to the cost price of 16 oranges, find the loss percent.
Solution
\[\text { Let the cost price of one orange be Rs . C, and its selling price be Rs }. S\]
\[\text { Therefore,} 16C = 18S\]
\[C = \frac{18}{16}S\]
\[\text { As cost price is more than the selling price, } \]
\[S . P . = \left( \frac{100 - \text { loss % }}{100} \right)C . P\]
\[S = \left( \frac{100 - \text { loss % }}{100} \right)C\]
\[\frac{S}{C} = \left( \frac{100 - \text { loss % }}{100} \right)\]
\[\frac{16}{18} = \left( \frac{100 - \text { loss % }}{100} \right)\]
\[\frac{1600}{18} = 100 -\text { loss % }\]
\[\text { Loss % } = 100 - \frac{1600}{18}\]
\[\text { Loss % }= \frac{1800 - 1600}{18}\]
\[ = \frac{200}{18} = \frac{100}{9}\]
\[ = 11\frac{1}{9}\]
\[\text { Therefore, the loss percent is 11 }\frac{1}{9} . \]%
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