X, Y are two points in a river. Points P and Q divide the straight line XY into three equal parts. The river flows along XY and the time taken by a boat to row from X to Q and from Y to Q are in the ratio 4 : 5. The ratio of the speed of the boat downstream to that of the river current is equal to:
Answer & explanation
Correct answer: option 2
We know that,
Upstream Speed = Speed of Boat – Speed of current
Downstream Speed = Speed of Boat + Speed of current
Given =
XP = PQ = QY
Ratio of time taken by boat to go from X to Q and Y to Q = 4 : 5
Let XP = PQ = QY = d
Let the speed of the boat = a km/h
Let the speed of the current = b km/h
As per the question:
= \(\frac{\frac{2d}{a + b}}{\frac{d}{a - b}}\) = \(\frac{4}{5}\)
= \(\frac{2(a - b)}{ (a + b)}\) = \(\frac{4}{5}\)
= 14b = 6a
= \(\frac{a}{b}\) = \(\frac{7}{3}\)
Speed of the boat downstream = (7 + 3) = 10
Speed of the current = 3