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.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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