By selling 90 ball pens for Rs 160 a person loses 20%. How many ball p

1.	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» S.P. of 90 ball pens = Rs 160, Loss = 20% \(\therefore\) C.P. of 90 ball pens = Rs \(\frac{160\times100}{(100-20)}\) = Rs \(\frac{160\times100}{80}\) = Rs 200 \(\therefore\) C.P. of 1 ball pen = Rs \(\frac{20}{9}\) Suppose x ball pens are sold to earn a profit of 20%. Then, C.P. of x ball pens = Rs \(\frac{20}{9}X\) S.P. of x ball pens = Rs 96 \(\therefore\) Profit = Rs\(\Big(96-\frac{20}{9}X\Big)\) Given, profit % = 20% \(\therefore\) \(\frac{\Big(96-\frac{20}{9}X\Big)}{\frac{20X}{9}}\) x 100 = 20 \(\Rightarrow\) \(\big(96-\frac{20X}{9}\big)\)x 5 = \(\frac{20X}{9}\) \(\Rightarrow\) 96 - \(\frac{20X}{9}\) = \(\frac{4X}{9}\) \(\Rightarrow\) \(\frac{24X}{9}\) = 96 \(\Rightarrow\) x = \(\frac{96\times9}{24}\) = 36. \(\therefore\) 36 ball pens should be sold for Rs 96 to earn a profit of 20%

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»

S.P. of 90 ball pens = Rs 160, Loss = 20%

\(\therefore\) C.P. of 90 ball pens = Rs \(\frac{160\times100}{(100-20)}\) = Rs \(\frac{160\times100}{80}\) = Rs 200

\(\therefore\) C.P. of 1 ball pen = Rs \(\frac{20}{9}\)

Suppose x ball pens are sold to earn a profit of 20%.

Then, C.P. of x ball pens = Rs \(\frac{20}{9}X\)

S.P. of x ball pens = Rs 96

\(\therefore\) Profit = Rs\(\Big(96-\frac{20}{9}X\Big)\)

Given, profit % = 20%

\(\therefore\) \(\frac{\Big(96-\frac{20}{9}X\Big)}{\frac{20X}{9}}\) x 100 = 20 \(\Rightarrow\) \(\big(96-\frac{20X}{9}\big)\)x 5 = \(\frac{20X}{9}\)

\(\Rightarrow\) 96 - \(\frac{20X}{9}\) = \(\frac{4X}{9}\) \(\Rightarrow\) \(\frac{24X}{9}\) = 96

\(\Rightarrow\) x = \(\frac{96\times9}{24}\) = 36.

\(\therefore\) 36 ball pens should be sold for Rs 96 to earn a profit of 20%