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 $20\%$?

S.P of 90 ball pens = Rs. 160
$\therefore$ S.P of 1 ball pen $=Rs.\frac{160}{90}=Rs.\frac{16}{9}$
Loss $=20\%$
$\therefore$ C.P of one pen $=\frac{S.P\times 100}{100-loss\%}=\frac{16\times 100}{9(100-20)}=Rs.\frac{16\times 100}{9\times 80}=Rs.\frac{20}{9}$
In second case,
Gain $=20\%$
S.P of one pen $=\frac{C.P\times (100+gain\%)}{100}$
$=\frac{20}{9}\times \frac{(100+20)}{100}=Rs.\frac{20}{9}\times \frac{120}{100}=Rs.\frac{8}{3}$
In $Rs.\frac{8}{3}$, ball pens will be sold = 1
$\therefore$ in Rs. 96, ball pens will be sold $=1\times \frac{3}{8}\times 96$
$=36$