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Question
The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.
Solution
\[\text { Let the cost price of one article be Rs . C and the selling price be Rs . S }\]
\[ \text { Therefore, }10C = 9S\]
\[C = \frac{9}{10}S\]
\[\text { So, the cost price is less than the selling price }. \]
\[S . P . = \left( \frac{100 + \text { Profit } %}{100} \right)C . P\]
\[S = \left( \frac{100 +\text { Profit } %}{100} \right)C\]
\[\frac{S}{C} = \left( \frac{100 +\text { Profit } %}{100} \right)\]
\[\frac{10}{9} = \left( \frac{100 + \text { Profit } %}{100} \right)\]
\[\frac{1000}{9} = 100 + \text { Profit } % \]
\[\frac{1000}{9} - 100 = \text { Profit } % \]
\[\text { Profit % }= \frac{1000 - 900}{9}\]
\[ = 11\frac{1}{9}\]
\[\text { Therefore, the required profit percent is 11 }\frac{1}{9} \]%.
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