Time taken by a boat to cover 90 km upstream is 2.5 hours more than that of same distance cover in downstream. If the ratio of Speed of boat in still water to stream is 5 : 1, then find the still water speed of the boat (in km/hr)?

Correct option is C

Information Given:

90 km upstream takes 2.5 hrs more than same downstream.

Ratio of speed of boat in still water to stream = 5:1.

Concept/Formula Used:

Upstream speed = (u - v), Downstream speed = (u + v).

Time = Distance / Speed.

For difference in time: (Distance)/(u-v) - (Distance)/(u+v) = time difference.

Explanation:

Let boat speed in still water = 5x, stream speed = x.

Upstream speed = 5x - x = 4x, Downstream speed = 5x + x = 6x.

So:

(90/4x) - (90/6x) = 2.5

Take LCM: (90×(6x-4x))/(4x×6x) = 2.5

=> (90×2x)/(24x2) = 2.5

=> (180x)/(24x2) = 2.5

=> 180/(24x) = 2.5

=> 180 = 60x

=> x = 3

So, still water speed = 5x = 15 km/hr