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 the running train? (Bank P.O., 2006) I. The length of the train is 180 metres. II. The train crosses another stationary train of 120 metres length in 60 seconds.

### Concept & Speed Formula To find the speed of a train crossing a stationary train, we divide the sum of their lengths by the time taken to cross. $$Speed = \frac{Length_1 + Length_2}{Time}$$ ### Step-by-Step Solution * **Question Stem:** Asks for the speed of the running train. No numerical data is given. * **Analyze Statement I:** The length of the running train ($L_1$) is 180 metres. Missing time and the length of any obstacle. Statement I alone is insufficient. * **Analyze Statement II:** The train crosses a stationary train ($L_2 = 120$ m) in $60$ seconds. Missing the length of the running train. Statement II alone is insufficient. * **Combine Statements I & II:** * $L_1 = 180$ m, $L_2 = 120$ m, $Time = 60$ s. * $Total\ Distance = 180 + 120 = 300$ m. * $Speed = \frac{300}{60} = 5$ m/s. * Since combining the statements allows us to solve the equation completely, both are necessary. ### Exam Strategy & Shortcut This is a standard template question. Speed requires Distance and Time. Distance here is the sum of two train lengths. Statement I provides part of the distance. Statement II provides the rest of the distance and the time. Both are unequivocally required to compute the answer. ### Common Pitfall A standard error is attempting to calculate speed using only Statement II by mistakenly assuming the running train behaves like a point object, ignoring its length. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**