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:

10 : 3

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