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Discussion :: Problems on Trains

  1. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

    2. A.
    45 m
    B.
    50 m
    C.
    54 m
    D.
    72 m

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    Answer : Option B

    Explanation :

    2 kmph = 1-sym-oparen-h1 2 x 5 1-sym-cparen-h1 m/sec = 5 m/sec.
    18 9
    4 kmph = 1-sym-oparen-h1 4 x 5 1-sym-cparen-h1 m/sec = 10 m/sec.
    18 9

    Let the length of the train be x metres and its speed by y m/sec.

    Then, 1-sym-oparen-h1 x 1-sym-cparen-h1 = 9 and 1-sym-oparen-h1 x 1-sym-cparen-h1 = 10.
    y - 5
    9
    y - 10
    9

    Therefore 9y - 5 = x and 10(9y - 10) = 9x

    => 9y - x = 5 and 90y - 9x = 100.

    On solving, we get: x = 50.

    Therefore Length of the train is 50 m.

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