UPSC CDS II 2024 Math Paper

Concept:Work and time problem where we need to find the combined work rate of $A$, $B$, and $C$, but the given statements only provide pair-wise rates.Explanation:Let the total work be $1$ unit.From Statement-I: $A + B$ together finish in $24$ days, so their one‑day work is $\frac{1}{24}$.From Statement-II: $B + C$ together finish in $36$ days, so their one‑day work is $\frac{1}{36}$.We need the one‑day work of $A + B + C$ together, say $\frac{1}{x}$.Notice that the combined rate of $A+B+C$ is not simply the sum of the two given rates, because $B$ is counted twice.In fact, $\frac{1}{x} = \big(\frac{1}{24} + \frac{1}{36}\big) - \text{work of }B\text{ alone}$.We have no information about $B$'s individual work rate from either statement.Therefore, even using both statements together, we cannot find a unique value for $\frac{1}{x}$.The question cannot be answered by the given data.Answer:Option D: The Question cannot be answered even by using both the Statements together.