The cost price of 10 articles is equal to the selling price of 9 articles.

Let the cost price of one article be Rs. C and the selling price be Rs. S

Therefore, $10 \mathrm{C}=9 \mathrm{~S}$

$\mathrm{C}=\frac{9}{10} \mathrm{~S}$

So, the cost price is less than the selling price.

S. P. $=\left(\frac{100+P \text { rofit } \%}{100}\right)$ C. P

$\mathrm{S}=\left(\frac{100+P \text { rofit } \%}{100}\right) \mathrm{C}$

$\frac{\mathrm{S}}{\mathrm{C}}=\left(\frac{100+P \text { rofit } \%}{100}\right)$

$\frac{10}{9}=\left(\frac{100+P \text { rofit } \%}{100}\right)$

$\frac{1000}{9}=100+P$ rofit $\%$

$\frac{1000}{9}-100=P$ rofit $\%$

$P$ rofit $\%=\frac{1000-900}{9}$

$=11 \frac{1}{9}$

Therefore, the required profit percent is $11 \frac{1}{9} \%$.