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    Question

    A boat covers 140 km downstream

    and 80 km upstream in 4.5 hours. Additionally, it takes 5.25 hours to travel 224 km downstream and 50 km upstream. Calculate the distance the boat would travel in still water in 2.4 hours.
    A 125.5 km Correct Answer Incorrect Answer
    B 115.2 km Correct Answer Incorrect Answer
    C 165.2 km Correct Answer Incorrect Answer
    D 100.5 km Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the upstream and downstream speed of boat be 'U' km/h and 'D' km/h respectively. ATQ: (140/D) + (80/U) = 4.5 --------- (I) And, (224/D) + (50/U) = 5.25 -------- (II) On solving, 5 X equation (I) - 8 X equation (II) , we get, 5 X [(140/D) + (80/U) ] - 8 X [(224/D) + (50/U) ] = 5 X 4.5 - 8 X 5.25 Or, (700/D) + (400/U) - (1,792/D) - (400/U) = 22.5 - 42 Or, (1,092/D) = 19.5 Or, 'D' = (1,092/19.5) = 56 On putting value of 'D' in equation (I) , We get, (140/56) + (80/U) = 4.5 Or, 2.5 + (80/U) = 4.5 Or, (80/U) = 2 So, 'U' = 40 Speed of boat in still water = (1/2) X (downstream speed + upstream speed) = (1/2) x (56 + 40) = (96/2) = 48 km/h Therefore, required distance = 48 X 2.4 = 115.2 km

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