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    Question

    The question consists of two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question or not.

    Find the length of train Y? Statement I: Train X

    takes 1 minute to cross a platform of length 1000 meters and 35 seconds to cross a pole. Train Y, moving in the opposite direction to Train X, crosses it in 30 seconds. Statement II: Train Y takes 50 seconds to cross a platform 900 meters long and 40 seconds to cross Train Z, which has a length of 1920 meters and is moving in the opposite direction.
    A Statement I alone is sufficient to answer the question Correct Answer Incorrect Answer
    B Statement II alone is sufficient to answer the question Correct Answer Incorrect Answer
    C Both statements together are necessary to answer the question Correct Answer Incorrect Answer
    D Either statement I alone or statement II alone is sufficient to answer the question Correct Answer Incorrect Answer
    E Both statements together are not sufficient to answer the question Correct Answer Incorrect Answer

    Solution

    Statement I: Train X crosses a platform of length 1000 meters and a pole in 1 minute and 35 seconds. So train X travel 1000 meters in 25 seconds (60 – 35) Speed of train X = 1000/25 = 40 m/s So length of train X = 40 x 35 = 1400 meters Also, (1400 + length of train Y) = (40 + speed of train Y) x 30 1400 + length of train Y = 1200 + 30 x speed of train Y Length of train Y = 30 x speed of train Y –200………….. (a) This statement alone is not sufficient to answer the question Statement II: Train Y crosses a platform of length 900 meters and train Z having a length of 1920 meters running in the opposite direction in 50 seconds and 40 seconds respectively. Length of train Y + 900 = speed of train Y x 50…………. (1) Also, length of train Y + 1920 = (speed of Y + speed of Z) x 40……….. (2) On solving both equations we got 1020 = 40 x speed of Z –10 x speed of Y 102 = 4 x speed of Z – the speed of Y………….. (3) This statement alone is not sufficient to answer On combining (I + II), Length of train Y = 30 x speed of train Y –200………… (a) Length of train Y + 900 = speed of train Y x 50…………. (1) So, 30 x speed of train Y –200 + 900 = speed of train Y x 50 20 x speed of train Y = 700 Speed of train Y = 700/20 = 35 m/s So length of train Y = 30 x 35 – 200 = 850 meters Both statements together is necessary to answer the question. Hence answer is option C

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