A and B are two points in a river. Point X and Y divide the line AB in three equal parts. Let the flow of the river is from A to B. The ratio of the time taken to row from point A to Y and from B to Y is 3 : 4. Find the ratio of the speed of the boat upstream to the flow of the river.
Answer & explanation
Correct answer: option 2
A---------X---------Y----------B
Here, AX = XY = YB = d
Speed of boat = u km/hr
Speed of river = v km/hr
Speed of boat in downstream(DS) = u + v
Speed of boat in upstream(US) = u - v
Time = \(\frac{Distance}{Speed}\)
According to question:
The ratio of the time taken to row from point A to Y and from B to Y = 3 : 4.
⇒ \(\frac{2d}{u\;+\;v}\) : \(\frac{d}{u\;-\;v}\) = 3 : 4
⇒ \(\frac{2(u\;-\;v)}{u\;+\;v}\) = \(\frac{3}{4}\)
⇒ 8(u - v) = 3(u + v)
⇒ 5u = 11v
⇒ u : v = 11 : 5
Speed of boat in upstream = u - v = 11 - 5 = 6
Speed of river = v = 5
Ratio of speed of boat in upstream to speed of river = 6 : 5