An article was sold at a certain price. Had it been sold at $\frac{4}{5}$ of that price, there would have been a loss of 10%. At what profit percentage was the article sold initially?

12.5

Let SP =  50x

Loss = 10%

New SP = 50x × \(\frac{4}{5}\) = 40x

CP = 40x × \(\frac{10}{9}\) = \(\frac{400x}{9}\)

Ratio of CP to SP = \(\frac{400x}{9}\) : 500x = 40 : 45

Profit % = \(\frac{45 - 40}{40}\)× 100 = 12.5%