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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 :

     

    2kmph = \((2\times\frac{5}{18})m/sec = (\frac{5}{9})m/sec \)

    4kmph = \((4\times\frac{5}{18})m/sec = (\frac{10}{9})m/sec \)

     

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

     

    Then, \(\left(\frac{X}{Y-\frac{5}{9}}\right)=9 \) and  \(\left(\frac{X}{Y-\frac{10}{9}}\right)=10\)

     


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

     

    On solving, we get: x = 50.

     

    Therefore Length of the train is 50 m

     

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