A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.

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boat = 10 km/hr and stream = 4 km/hr

boat = 6 km/hr and stream = 4 km/hr

boat = 8 km/hr and stream = 6 km/hr

boat = 8 km/hr and stream = 4 km/hr

answer is D.

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Detailed Solution

Given that a boat goes 16 km upstream and 24km downstream in 6hrs.
Therefore,
Time Taken to go 16km upstream + Time taken to go 24km Downstream = 6hrs.
Let the speed of the boat in still water be

u km / hr

and the speed of the stream be

v km / hr

.
Now,
Speed Downstream

= u + v

and,
Speed upstream

= u − v

.
We know that,

Speed = distance Time ⇒ Time = distance speed ∴ 16 u − v + 24 u + v = 6

Let us find the speed of boat in upstream.

⇒ 16 u − v + 24 u + v = 6 ⇒ 2 8 u − v + 12 u + v = 6 ⇒ 8 u − v + 12 u + v = 3 ⇒ 8 u + 8 v + 12 u − 12 v u 2 − v 2 = 3 ⇒ 20 u − 4 v 3 = u 2 − v 2 ............ (1)

Similarly, let us find the speed of boat in downstream.

⇒ 12 u − v + 36 u + v = 6 ⇒ 6 2 u − v + 6 u + v = 6 ⇒ 2 u − v + 6 u + v = 1 ⇒ 2 u + 2 v + 6 u − 6 v u 2 − v 2 = 1 ⇒ 8 u − 4 v = u 2 − v 2 .............. (2)

Comparing (1) and (2), we get

⇒ 8 u − 4 v = 20 u − 4 v 3 ⇒ 24 u − 12 v = 20 u − 4 v ⇒ 4 u = 8 v ⇒ u = 2 v

Substitute u = 2v in equation (1).

⇒ 16 u − v + 24 u + v = 6 ⇒ 2 8 2 v − v + 12 2 v + v = 6 ⇒ 8 v + 12 3 v = 3 ⇒ 24 + 12 3 v = 3 ⇒ 9 v = 36 ⇒ v = 4

We know that, u = 2v.
But v = 4 km/hr.
So, u = 8 km/hr.
Therefore, speed of a boat in still water = 8 km/hr and speed of stream = 4 km/hr.
The correct option is (4).

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