A boat covers a round trip journey between two points A and B in a river in T hours. If its speed in still water becomes 2 times, it would take T hours for the same journey. Find the ratio of its speed in still water to the speed of the river.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 11 : 1.
Let the speed of the boat in still water = x km/h
The speed of the stream = y km/h
Downstream = x + y km/h
Upstream = x - y km/h
Time = Distance/Speed
Now according to the question,
D/(x + y) + D/(x - y) = T
⇒ D.2x/(x2 - y2) =T
⇒ D/T = (x2 - y2)/2x.........(1)
⇒ D/(2x + y) + D/(2x - y) = 80T/161
⇒ D.4x/(4x2 - y2) = 80T/161
⇒ D/T = (80/161).(4x2 - y2)/4x ...........(2)
From eq. (1) and (2)
⇒ (x2 - y2)/2x = (80/161)(4x2 - y2)/4x
⇒ (x2 - y2) = (40/161)(4x2 - y2)
⇒ 161 x2 - 161 y2 = 160 x2 - 40 y2
⇒ x2 = 121 y2
⇒ x2/y2 = 121
⇒ x/y = 11/1
So, the required ratio = 11 : 1