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    Question

    The speeds of two trains, P and

    Q, are in the ratio of 4:5. The length of train P is 300 meters. What is the speed of train Q? Statement I: Trains P and Q can cross each other in 20 seconds when they are moving in opposite directions. Statement II: Train P can cross a dog running in the opposite direction at a speed of 10 km/h in 20 seconds. The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
    A 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. Correct Answer Incorrect Answer
    B 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. Correct Answer Incorrect Answer
    C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
    D The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

    Solution

    ATQ, Let the speed of trains ‘P’ and ‘Q’ be 4x km/hr and 5x km/hr, respectively Statement I: According to the question, Let the length of train ‘Q’ be ‘l’ metres (4x + 5x) × (5/18) = (300 + l)/20 Or, 100x = 600 + 2l So, data in statement I alone is not sufficient to answer the question. Statement II: (4x + 10) × (5/18) = 300/20 Or, 20x + 50 = 18 × 15 = 270 Or, 20x = 220 Or, x = 11 Therefore, speed of train ‘Q’ = 5x = 55 km/hr So, data in statement II alone is sufficient to answer the question. So, 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

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