Question

By selling 90 ballls for rs.160 a person loses 20%.The number of ball which should be sold for rs.96 so as to have a profit of 20% is

Answer 1

$\sf{\underline{Given:}}$

Selling price of 90 pens ${\sf= 160}$

Loss $\sf{= 20\%}$

Cost price of 90 pens:

$\implies$ $\sf{\frac{160 \times 100}{80}}$

$\implies$ $\sf{ \frac{16000}{80} }$

$\implies$ $\boxed{\sf{ 200}}$

$\sf{\underline{Now:}}$

Cost price of a pen:

$\implies$ $\sf{\frac{200}{90} }$

$\implies$ $\sf{\frac{20}{9}}$

$\sf{\underline{Therefore:}}$

Cost price of a pen is $\boxed{\sf{ \frac{20}{9}}}$

$\sf{\underline{Note:}}$ For a profit of 20%, x pens should be sold for Rs. 96

$\sf{\underline{So:}}$

Cost price of x pens must be:

$\implies$ $\sf{ \frac{96 \times 100}{120}}$

$\implies$ $\sf{ \frac{9600}{120}}$

$\implies$ $\boxed{\sf{ 80}}$

$\sf{\underline{That\:is:}}$

Cost price of a pen must be: $\boxed{\sf{ \frac{80}{x}}}$

$\sf{\underline{Now:}}$

$\implies$ $\sf{\frac{20}{9} = \frac{80}{x}}$

$\implies$ $\sf{20 \times x = 80 \times 9}$

$\implies$ $\sf{20x = 720}$

$\implies$ $\sf{x = \frac{720}{20} }$

$\implies$ $\sf{x = \frac{72}{2}}$

$\implies$ $\boxed{\sf{x = 36}}$

$\sf{\underline{Thus:}}$

36 ball pens should be sold at Rs. 96 to earn a profit of 20%