By selling an article at$$\frac 4{10}$$​ of its actual selling price, Nirbhay incurs a loss of 28%. It he sells it at 82% of its actual selling price, then the profit percentage is:

Correct option is A

​$$\textbf{Given:} \\\text{First selling price} = \dfrac{4}{10} \text{ of actual selling price} \\\text{Loss} = 28\% \\\text{Second selling price} = 82\% \text{ of actual selling price}\\\textbf{Formula Used:} \\\text{Loss\%} = \dfrac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \\\text{Profit\%} = \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100\\\textbf{Solution:} \\\text{Let the actual selling price be } ₹100\\\text{Then, first selling price} = \dfrac{4}{10} \times 100 = ₹40\\\text{Given loss } = 28\% \\\Rightarrow \text{SP} = 72\% \text{ of CP}\\\text{So,} \\40 = 72\% \text{ of CP} \\40 = 0.72 \times \text{CP} \\\text{CP} = \dfrac{40}{0.72} = \dfrac{4000}{72} = \dfrac{500}{9}\\\text{Second selling price} = 82\% \text{ of actual selling price} = 0.82 \times 100 = ₹82\\\text{Profit} = \text{SP} - \text{CP} = 82 - \dfrac{500}{9} = \dfrac{738 - 500}{9} = \dfrac{238}{9}\\\text{Profit\%} = \dfrac{\frac{238}{9}}{\frac{500}{9}} \times 100 \\= \dfrac{238}{500} \times 100 \\= 47.6\%\\\textbf{Profit Percentage} = \boxed{47.6\%}$$​​