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%?

Answer 1

\[\text { S . P of 90 ball pens = Rs . 160 }\]

\[\text { Loss = 20 % } \]

\[\text{Therefore, C . P = SP }\left( \frac{100}{100 -\text {  loss % }} \right)\]

\[CP = \frac{100}{100 - 20} \times 160\]

\[ = \frac{16000}{80}\]

\[ = Rs . 200\]

\[\text { Now, } \]

\[\text { S . P of 90 ball pens = Rs . 96 }\]

\[\text { Profit = 20 % } \]

\[ \text { C . P = SP }\left( \frac{100}{100 + \text { Profit % }} \right)\]

\[CP = \frac{100}{100 + 20} \times 96\]

\[ = \frac{9600}{120}\]

\[ = \text { Rs . 80 }\]

\[\text { Rs . 200 is the C . P of 90 ball pens } . \]

\[\text { Therefore, Rs . 80 is the C . P of } = \frac{90 \times 80}{200} = \text { 36 ball pens }\]

\[\text { Thus, 36 ball pens should be sold at Rs . 96 to earn a profit of 20 % }.\]