An article is sold at a certain price. If it is sold at 80% of this price, then there will be a loss of 10%. What is the percentage profit when the article is sold at the original selling price?

$$\eqalign{ & {\text{Let price}} = 100 \cr & {\text{Sold}} = 100 \times \frac{{80}}{{100}} = 80 \cr & {\text{Cost price}} = \frac{{80 \times 100}}{{90}} = \frac{{800}}{9} \cr & {\text{Cost price : Selling price}} \cr & = \frac{{800}}{9}:100 \cr & = 800:900 \cr & {\text{Profit }}\% = \frac{{100}}{{800}} \times 100 = 12\frac{1}{2}\% \cr} $$