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. What is the speed of a running train? I. The train crosses a signal post in 6 seconds. II. The train crosses another train running in the opposite direction in 15 seconds.

### Concept & Logic To find the speed of a single train, we need to know its length and the time it takes to cross a stationary point, or sufficient information to isolate its speed from relative speed equations. $$Speed = \frac{Length}{Time}$$ ### Step-by-Step Solution * Let the speed of the train be $S_1$ and its length be $L_1$. * From Statement I: The train crosses a post in 6 seconds. Therefore, $S_1 = \frac{L_1}{6}$. We have two unknown variables ($S_1$ and $L_1$). This statement is insufficient alone. * From Statement II: The train crosses another train in 15 seconds. The formula is $15 = \frac{L_1 + L_2}{S_1 + S_2}$. This introduces two new unknown variables: the length of the second train ($L_2$) and the speed of the second train ($S_2$). This statement is insufficient alone. * Combining both statements: We have four unknown variables ($S_1, L_1, S_2, L_2$) but only two equations. We cannot determine the value of $S_1$. ### Exam Strategy & Shortcut Whenever a new statement introduces new variables (like a completely undefined second train) without providing their values, you will generally not be able to solve the system of equations. Immediately mark it as insufficient. ### Common Pitfall A common mistake is assuming that because both statements involve crossing times, they can magically resolve into a single speed without realizing the lengths of the trains are completely missing. ### 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**.