UPSC CDS II 2024 Math Paper

Concept:Expenditure = Price × Consumption. To keep expenditure constant, a percentage increase in price must be offset by a percentage decrease in consumption, which depends only on the percentage price increase, not on absolute values.Explanation:Let original price be $P$ and original consumption be $C$.New price after $20\%$ hike: $P_{\text{new}} = P + 0.20P = 1.20P$.Since expenditure remains same: $P \times C = P_{\text{new}} \times C_{\text{new}}$.Thus, $C_{\text{new}} = \frac{P \times C}{1.20P} = \frac{C}{1.20}$.Reduction in consumption: $C - \frac{C}{1.20} = C \left(1 - \frac{1}{1.20}\right)$.Percentage reduction = $\frac{C \left(1 - \frac{1}{1.20}\right)}{C} \times 100 = \left(1 - \frac{1}{1.20}\right) \times 100$.Simplify: $\left(\frac{1.20 - 1}{1.20}\right) \times 100 = \frac{0.20}{1.20} \times 100 = \frac{1}{6} \times 100 \approx 16.67\%$.The calculation uses only the percentage price increase (20%). No actual price or consumption values are needed. Hence, both statements are unnecessary.Answer:The Question can be answered even without using any of the Statements. Thus, the correct option is D.