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    Question

    Train 'P' can cross a pole in 8 seconds and a 160 metres

    long bridge in 12 seconds. Train 'Q' whose length is 60% of the length of train 'P' runs in the same direction of train 'P'. If train 'Q' crosses train 'P' in 16 seconds, then find the speed of train 'Q'.
    A 68 m/s Correct Answer Incorrect Answer
    B 72 m/s Correct Answer Incorrect Answer
    C 75 m/s Correct Answer Incorrect Answer
    D 80 m/s Correct Answer Incorrect Answer
    E 85 m/s Correct Answer Incorrect Answer

    Solution

    Let the length and the speed of the train 'P' be 'x' metres and 's' m/s.
    ATQ,
    (x/s) = 8
    So, 'x' = 8s.........(i)
    Also, {(x + 160) ÷ s} = 12
    Or, 8s + 160 = 12s [from equation (i)]
    Or, 160 = (12s - 8s)
    Or, 's' = (160/4) = 40
    Length of train 'P' = (8 × 40) = 320 metres
    So, length of train 'Q' = (320 × 0.60) = 192 metres
    Let the speed of train 'Q' be 'q' m/s.
    ATQ,
    (320 + 192) ÷ (q - 40) = 16
    Or, 512 = 16 × (q - 40)
    Or, (q - 40) = 32
    So, 'q' = 32 + 40 = 72
    Therefore, speed of train 'Q' = 72 m/s

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