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    Question

    The total time taken by a boat to cover (d+30) km in

    downstream and (d-60) km in upstream is (t+3) hours. The speed of stream is one fourth of the speed of boat in downstream. The same boat can cover ‘d’ distance in still water in (t-8) hours. If the speed of stream is 15 km/h, then find out the value of ‘t’.
    A 16 Correct Answer Incorrect Answer
    B 20 Correct Answer Incorrect Answer
    C 24 Correct Answer Incorrect Answer
    D 12 Correct Answer Incorrect Answer
    E None of the above Correct Answer Incorrect Answer

    Solution

    The speed of stream is one fourth of the speed of boat in downstream.

    If the speed of stream is 15 km/h.

    15 = (¼) of speed of boat in downstream

    speed of boat in downstream = 60 km/h

    Speed of boat in still water = 60-15 = 45 km/h

     The same boat can cover ‘d’ distance in still water in (t-8) hours.

    d = 45(t-8)    Eq.(i)

    The total time taken by a boat to cover (d+30) km in downstream and (d-60) km in upstream is 

    (t+3) hours.

    [(d+30)/60] + [(d-60)/(45-15)] = (t+3)

    [(d+30)/60] + [(d-60)/30] = (t+3)

    Put the value of ‘d’ from Eq.(i) in the above equation.

    [(45(t-8)+30)/60] + [(45(t-8)-60)/30] = (t+3)

    [(45t-360+30)/60] + [(45t-360-60)/30] = (t+3)

    [(45t-330)/60] + [(45t-420)/30] = (t+3)

    [0.75t-5.5] + [1.5t-14] = (t+3)

    2.25t-19.5 = t+3

    2.25t-t = 19.5+3

    1.25t = 22.5

    Value of ‘t’ = 18

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