UPSC CDS 1 2023 Math Paper

Concept:The problem calculates the hypothetical profit percentage if no bananas were lost, using the same selling price per banana as in the actual scenario.Explanation:Assume the vendor buys 100 bananas at a cost of $₹1$ each, so total cost price (CP) is $\text{Rs.}100$.During transportation, $12\%$ of the bananas are lost, i.e., $12$ bananas.Remaining bananas $= 100 - 12 = 88$.The vendor sells these 88 bananas at a $4\%$ overall profit on the total cost.Thus, total selling price (SP) of 88 bananas $= 100 \times (1 + \frac{4}{100}) = ₹104$.Selling price per banana $= \frac{104}{88} = \frac{13}{11}$.If no bananas were lost, the vendor would sell all 100 bananas at the same price per banana, i.e., $₹\frac{13}{11}$ each.Total SP for 100 bananas $= 100 \times \frac{13}{11} = ₹\frac{1300}{11} \approx ₹118.18$.Profit $= \frac{1300}{11} - 100 = ₹\frac{200}{11}$.Profit percentage $= \frac{\frac{200}{11}}{100} \times 100\% = \frac{200}{11}\% = 18\frac{2}{11}\%$.Answer:$18\frac{2}{11}\%$ (Option C).