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 speed of the train? I. The train passes a man walking at the rate of 3 kmph in 9 seconds. II. The train passes a man walking at the rate of 6 kmph in 10 seconds. III. The train is moving in the same direction in which the two men are moving.

### Concept & Logic When a train crosses a moving person, the relative speed is the difference (if moving in the same direction) or sum (if moving in opposite directions) of their speeds. $$ \text{Relative Speed} = v \pm u $$ ### Step-by-Step Solution * Let the train's length be $x$ and its speed be $v$. * **From Statement I:** The relative speed is related to the man walking at 3 kmph. $x = 9 \times (v \pm 3)$. We don't know the direction. * **From Statement II:** The relative speed is related to the man walking at 6 kmph. $x = 10 \times (v \pm 6)$. We still don't know the direction. * **From Statement III:** Both men and the train are moving in the same direction. This clarifies the relative speeds to $(v - 3)$ and $(v - 6)$. * Using all three statements: $9(v - 3) = 10(v - 6)$. This linear equation allows us to solve for $v$. ### Exam Strategy & Shortcut Immediately identify missing variables. Statements I and II give time and object speed, but lack relative direction. Statement III gives the direction but provides no numerical values. All three must be combined to form a solvable, unambiguous equation. ### Common Pitfall Assuming the direction is the "same" by default without Statement III, which would incorrectly lead to choosing "I and II only". ### Final Answer Therefore, the correct answer is **All I, II and III**.