UPSC CDS 2 2023 Math Paper

Concept:Profit percentage is calculated as $\frac{\text{Profit}}{\text{Cost Price}} \times 100\%$, where Profit = Selling Price − Cost Price.Explanation:Let the original cost price (CP) be $100$.At a profit of $20\%$, the selling price (SP) is $100 + 20\%\text{ of }100 = 100 + 20 = 120$.If the article was bought at $20\%$ less, the new CP becomes $100 - 20\%\text{ of }100 = 100 - 20 = 80$.The selling price remains the same, i.e., $120$.Profit with the new CP = $120 - 80 = 40$.Profit percentage = $\frac{40}{80} \times 100\% = 50\%$.Alternatively, using the shortcut: $\frac{\text{SP}}{\text{CP}} = \frac{100+20}{100-20} = \frac{120}{80}$, so profit% = $\frac{(120-80)\times 100}{80}=50\%$.Answer:$50\%$