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    Question

    A boat covers a distance of 338

    km upstream in 13 hours. After rain, the speed of the stream increases by 50%, and the speed of the boat in still water decreases by 25% due to low visibility. Following this, the boat takes 7 hours to travel 294 km downstream. Determine the difference between the speed of the boat in still water after the rain and the speed of the stream after the rain.
    A 10 km/h Correct Answer Incorrect Answer
    B 20 km/h Correct Answer Incorrect Answer
    C 18 km/h Correct Answer Incorrect Answer
    D 12 km/h Correct Answer Incorrect Answer

    Solution

    ATQ, Let the speed of boat in still water before rain be x km/h. And, the speed of stream before rain be y km/h. So, the upstream speed before rain = (x – y) = 338 ÷ 13 x – y = 26 ------(i) Speed of boat in still water after rain = 0.75x km/h Speed of stream after rain = 1.5 y km/h Downstream speed of boat after rain = 0.75x + 1.5y = 294 ÷ 7 0.75x + 1.5y = 42 -------(ii) On solving (i) and (ii), we get x = 36 km/h and y = 10 km/h So, the speed of boat in still water after rain = 0.75 × 36 = 27 km/h Speed of stream after rain = 1.5 × 10 = 15 km/h Required difference = 27 – 15 = 12 km/h

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