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    Question

    Three friends namely  F, G and H are rowing their boats in a same river. Speeds of F and G in still water are 6 km/h more and 4 km/h more, respectively than speed of H in still water. Ratio of speed of G in downstream to speed of H in downstream is 4 : 3. Find the distance covered by H in 5 hours while going against the stream. Which of the following option alone is not sufficient to find the answer?

    I   The river is flowing at a rate of 2 km/h.

    II  Difference between upstream speed of F and H is 6 km/h. 

    III Ratio of upstream speed G and H is 3 : 2, respectively.

    IV  H covers 240 km downstream in 20 hours. 

    A Either I alone or III alone is not sufficient Correct Answer Incorrect Answer
    B Only II is not sufficient Correct Answer Incorrect Answer
    C Either II alone or IV alone is not sufficient Correct Answer Incorrect Answer
    D Only III alone is not sufficient Correct Answer Incorrect Answer
    E Only IV alone is not sufficient Correct Answer Incorrect Answer

    Solution

    Let the Speed in still water, of Boat H = x km/h,  Then Boat F = x + 6 km/h,  Boat G = x + 4 km/h  Let the Speed of stream = y km/h  (x + 4 + y)/(x + y) = 4/3  3x + 12 + 3y = 4x + 4y  x + y = 12 = Downstream speed of Boat H Therefore in Upstream,  Distance covered by Boat H= d = 5(x – y) From (I),  y = 2 km/h, x = 12 – 2 = 10 km/h, d = 5 × (10 – 2) = 40 km/h  From (II), (x + 6 – y) – (x – y) = 6  From (III),(x + 4 – y)/(x – y) = 3/2 2(x – y) + 8 = 3(x – y) x – y = 8 D = 5 × 8 = 40 km/h  From (IV),  x + y = 240/20 = 12 Hence, Either II alone or IV alone is not sufficient to answer the data

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