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    Question

    The ratio between the speed of the boat in upstream and

    the speed of the stream are 6:5 respectively. The boat can cover (d+140) km distance in downstream in 28 hours. The same boat can cover (d+100) km in still water in 40 hours. Find out the time taken by the same boat to cover (d-240) km distance in upstream.
    A 78 hours Correct Answer Incorrect Answer
    B 80 hours Correct Answer Incorrect Answer
    C 60 hours Correct Answer Incorrect Answer
    D 62 hours Correct Answer Incorrect Answer
    E None of the above Correct Answer Incorrect Answer

    Solution

    The ratio between the speed of the boat in upstream and the speed of the stream are 6:5 respectively.

    Let’s assume the speed of the boat in upstream and the speed of the stream are ‘6a‘ and ‘5a‘ respectively.

    Speed of boat in downstream = 6a+5a+5a = 16a

    Speed of boat in still water = 16a-5a = 11a

    The boat can cover (d+140) km distance in downstream in 28 hours.

    (d+140)/28 = 16a

    (d+140) = 448a

    d = 448a-140    Eq.(i)

    The same boat can cover (d+100) km in still water in 40 hours.

    (d+100)/40 = 11a

    (d+100) = 440a

    d = 440a-100    Eq.(ii)

    So Eq.(i) = Eq.(ii)

    448a-140 = 440a-100

    448a-440a = 140-100

    8a = 40

    a = 5

    Put the value of ‘a’ in Eq.(i).

    d = 448x5-140

    = 2240-140

    = 2100

    Time taken by the same boat to cover (d-240) km distance in upstream = (d-240)/(6a)

    Put the value of ‘d’ and ‘a’ in the above equation.

    = (2100-240)/(6x5)

    = 1860/30

    = 62 hours

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