281. Three towns X, Y, and Z are on a river which flows uniformly. Y is equidistant from X and Z. If a boats man rows from X to Y and back in 10 hours and X to Z in 4 hours, find the ratio of speed of the boats man in still water to the speed of the current.
A. 2:5
B. 5:3
C. 3:5
D. 1:2
✅ The correct answer is option B. 5:3.
X ———— Y ———— Z
X ———— Y ———— Z
If ‘d’ is the distance between X and Y, then ‘d’ is the distance between Y and Z.
Now the total time for the batsman to row from X to Z is 4 hours. Therefore, time to row from X to Y is 2 hours.
Also the time for the boats man to row from X to Y and back is 10 hours. Hence, time required to row from Y to X is 8 hours.
If, a: speed of boats man in still water
b: speed of the river
d/(a + b) = 2; d/(a – b) = 8
2*(a + b) = 8*(a – b)
a + b = 4a – 4b
3a = 5b
a:b = 5:3