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Question
By selling 90 ball pens for Rs 160 a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?
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Solution
\[\text { S . P of 90 ball pens = Rs . 160 }\]
\[\text { Loss = 20 % } \]
\[\text{Therefore, C . P = SP }\left( \frac{100}{100 -\text { loss % }} \right)\]
\[CP = \frac{100}{100 - 20} \times 160\]
\[ = \frac{16000}{80}\]
\[ = Rs . 200\]
\[\text { Now, } \]
\[\text { S . P of 90 ball pens = Rs . 96 }\]
\[\text { Profit = 20 % } \]
\[ \text { C . P = SP }\left( \frac{100}{100 + \text { Profit % }} \right)\]
\[CP = \frac{100}{100 + 20} \times 96\]
\[ = \frac{9600}{120}\]
\[ = \text { Rs . 80 }\]
\[\text { Rs . 200 is the C . P of 90 ball pens } . \]
\[\text { Therefore, Rs . 80 is the C . P of } = \frac{90 \times 80}{200} = \text { 36 ball pens }\]
\[\text { Thus, 36 ball pens should be sold at Rs . 96 to earn a profit of 20 % }.\]
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