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

Solution:

S. $P$ of 90 ball pens $=$ Rs. 160

Loss $=20 \%$

Therefore, C. $\mathrm{P}=\operatorname{SP}\left(\frac{100}{100-l \text { oss } \%}\right)$

$\mathrm{CP}=\frac{100}{100-20} \times 160$

$=\frac{16000}{80}$

$=$ Rs. 200

Now,

S.P of 90 ball pens $=$ Rs. 96

Profit $=20 \%$

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

$\mathrm{CP}=\frac{100}{100+20} \times 96$

$=\frac{9600}{120}$

$=$ Rs. 80

Rs. 200 is the C.P of 90 ball pens.

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

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