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%?
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 $20 \%$.