Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is /are sufficient to answer the given question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. A train crosses another train running in the opposite direction in $x$ seconds. What is the speed of the train? I. Both the trains have the same length and are running at the same speed. II. One train crosses a pole in 5 seconds.

### Concept & Logic To find the speed of a train, we need both its length and the time it takes to cross a stationary point, or sufficient relative speed data. $$Speed = \frac{Length}{Time}$$ ### Step-by-Step Solution * Let the speed of the train be $v$ and its length be $L$. * From Statement I: The second train also has length $L$ and speed $v$. Relative speed = $2v$. Total distance = $2L$. Time to cross = $\frac{2L}{2v} = \frac{L}{v} = x$. We can't find $v$ from this alone. * From Statement II: Time taken to cross a pole = $5$ seconds. Therefore, $\frac{L}{v} = 5$. * Combining both statements: From II, we know $\frac{L}{v} = 5$. This matches the equation from Statement I (meaning $x=5$), but it still leaves us with the ratio of length to speed, not the absolute value of the speed $v$. We have one equation and two variables ($L$ and $v$). ### Exam Strategy & Shortcut If equations only give you a ratio (like $\frac{L}{v}$) but no absolute values for either distance or speed, you can never find the individual values. Instantly mark as insufficient. ### Common Pitfall Mistakenly assuming that finding the value of $x$ (which is 5) means the problem is solved, overlooking that the question actually asks for the *speed* of the train, not the value of $x$. ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question**.