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    Question

    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. 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.
    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 тАУ 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 тАУ200тАжтАжтАжтАж.. (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 50тАжтАжтАжтАж. (1) Also, length of train Y + 1920 = (speed of Y + speed of Z) x 40тАжтАжтАж.. (2) On solving both equations we got 1020 = 40 x speed of Z тАУ10 x speed of Y 102 = 4 x speed of Z тАУ the speed of YтАжтАжтАжтАж.. (3) This statement alone is not sufficient to answer On combining (I + II), Length of train Y = 30 x speed of train Y тАУ200тАжтАжтАжтАж (a) Length of train Y + 900 = speed of train Y x 50тАжтАжтАжтАж. (1) So, 30 x speed of train Y тАУ200 + 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 тАУ 200 = 850 meters Both statements together is necessary to answer the question. Hence answer is option C

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