By selling an article at $\frac{7}{12}$ of its selling price, a man loses 16%. If he sells it at 90% of its original selling price, then what will be the profit percentage?

29.6%

By selling an article at $\frac{7}{12}$ of its selling price, a man loses 16% means,

\(\frac{SP}{Original\; SP}\) =  \(\frac{7x}{12x}\)

loss = 16%

So the CP = 

84% of the CP = 7x

100% of the CP = 7x × \(\frac{100}{84}\) = 8.33x

Now the original selling price = 12x

Final selling price = 90% of original SP = 90% of 12x = 10.8x

Profit % = ( 10.8x - 8.33x ) × \(\frac{100}{8.33x}\) = 29.6%