Directions : Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the length of the train X? I. Train X crosses a telegraph post in 20 seconds II. Train X crosses a platform of length 800 m in 100 seconds. III. Train X passes through a tunnel 400 m long in 60 seconds.

### Concept & Logic The length of a train can be determined if we have two independent mathematical relationships involving its speed and length. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution * Let the length of train X be $x$ meters and its speed be $v$ m/s. * **From Statement I:** Crossing a point object takes 20 seconds. $v = \frac{x}{20} \Rightarrow x = 20v$ * **From Statement II:** Crossing an 800 m platform takes 100 seconds. $v = \frac{x + 800}{100} \Rightarrow 100v = x + 800$ * **From Statement III:** Crossing a 400 m tunnel takes 60 seconds. $v = \frac{x + 400}{60} \Rightarrow 60v = x + 400$ * Combining I and II: We can substitute $v$ to solve for $x$. * Combining I and III: We can substitute $v$ to solve for $x$. * Combining II and III: We have two independent linear equations, which can be solved for $x$ and $v$. * Therefore, any combination of two statements yields the answer. ### Exam Strategy & Shortcut Recognize that each statement gives a unique linear equation with the same two variables ($x$ and $v$). In algebra, any set of two independent linear equations with two variables can be solved to find exact values. Thus, any pair works. ### Common Pitfall A common mistake is believing that all three statements are needed because the equations might seem dependent at first glance, or assuming statement I is mandatory because it's the simplest. ### Final Answer Therefore, the correct answer is **Any two of the three**.