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    Question

    A boat sails 180 km downstream and half of that distance

    upstream in 12 hours. If the stream’s speed is 50% less than that of the boat in still water, determine the time required to travel 75 km upstream and 225 km downstream.
    A 12 hrs Correct Answer Incorrect Answer
    B 15 hrs Correct Answer Incorrect Answer
    C 24 hrs Correct Answer Incorrect Answer
    D 10 hrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let, the speed of the boat in still water = 4x kmph

    Speed of the stream = 4x × (1 – 0.5) = 2x kmph

    Downstream speed of the boat = (4x + 2x) = 6x kmph

    Upstream speed of the boat = (4x – 2x) = 2x kmph

    Distance travelled in upstream = (1/2) × 180 = 90 km

    Now,

    (180 / 6x) + (90 / 2x) = 12

    Or, (30/x) + (45/x) = 12

    Or, (75/x) = 12

    So, x = 75 / 12 = 6.25

    Now,

    Upstream speed = 2x = 12.5 kmph

    Downstream speed = 6x = 37.5 kmph

    Time to travel 75 km upstream = 75 / 12.5 = 6 hours

    Time to travel 225 km downstream = 225 / 37.5 = 6 hours

    Total time = 12 hours

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