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 which takes 9 seconds to cross a signal post? I. The length of the train is 90 metres. II. The train takes 27 seconds to cross a platform of 180 metres.

### Concept & Equating Speed The speed of a train remains constant whether it crosses a point object (like a post) or a long object (like a platform). We can set up independent equations using the provided time to cross different objects. $$Speed = \frac{Length\ of\ Train}{Time\ to\ cross\ post}$$ $$Speed = \frac{Length\ of\ Train + Length\ of\ Platform}{Time\ to\ cross\ platform}$$ ### Step-by-Step Solution * **Question Stem:** The train crosses a signal post in 9 seconds. Let speed be $S$ and length be $L$. Equation: $S = \frac{L}{9} \implies L = 9S$. * **Analyze Statement I:** Length of the train ($L$) = 90 metres. * Substitute into stem equation: $S = \frac{90}{9} = 10$ m/s. * Statement I alone gives a specific answer. It is sufficient. * **Analyze Statement II:** The train crosses a 180 m platform in 27 seconds. * Equation: $S = \frac{L + 180}{27}$. * Substitute $L = 9S$ from the stem into this equation: $S = \frac{9S + 180}{27}$. * $27S = 9S + 180 \implies 18S = 180 \implies S = 10$ m/s. * Statement II alone also gives a specific answer. It is sufficient. ### Exam Strategy & Shortcut When a train crosses a post, the time taken ($9$s) represents the time to cover its own length. When it crosses a $180$m platform in $27$s, the extra time ($27 - 9 = 18$s) is exactly the time taken to cover the platform's length. $Speed = \frac{180}{18} = 10$ m/s. Statement II alone works. Statement I also clearly works ($90/9$). Thus, either is sufficient. ### Common Pitfall Students often fail to recognize that the question stem itself contains crucial algebraic information ($L = 9S$) and mistakenly believe Statement II has two unknown variables ($S$ and $L$), concluding it is insufficient. ### Final Answer Therefore, the correct answer is **if the data either in Statement I or in Statement II alone are sufficient to answer the question;**.