Aptitude - Boats and Streams - Discussion

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

i.e.
d=d
44/5 x = 4y
by further solving
11x - 5y =0 i.e. y=11/5x ---> eq(1)

They have x = speed of the boat - speed of the current = u-v.
And y = speed of boat + speed of the current = u + v.

From eq(1).
u-v = 11/5(u + v).
u/v = 8/3.
i.e. u:v = 8:3.

Well said, Thank you @Mahesh.

(x-y)8*48/60 = (x+y)4,
(x-y)8*4/5 = (x+y)4,
(44/5)x-(44/5)y = 4x+4y,
(44/5)x-4x = 4y+(44/5)y,
(44x-20x)/5 = (20y+44y)/5,
24x = 64y,
= 3 : 8.

I'm not getting this. Anyone, please help to understand the answer.

@Mallika B.

They have x = speed of the boat - speed of the current.
And y = speed of boat + speed of the current.
So y - × = 2 * (speed of boat),
Then (y-x)/2 = speed of the boat.

Can somebody please explain why have we done (y-x/2) in the required ratio step? If that is associated with downstream, why are we subtracting?

Please explain me.

Thank you. @Tushar Pawar.

Given,
Time (upstream)=8 hour 48 min=(8*60+48) = 528 min.
Time (downstream)= 4 hour = (4*60)min = 240 min.

Let distance be x.
we know speed =distance/time.
so, the speed of the boat (upstream) = distance/time.
= x/528.
speed of the boat (downstream) = distance/time.
= x/240.

We know that;
speed of boat in still water = (downstream+upstream)/2.
= (x/240 + x/528)/2.
= x/330.

We know that
speed of stream/current water.
= (downstream-upstream)/2.
So we have to find the ratio of the speed of the boat in still water by the speed of the stream/current =
(x/330)/(x/528)=8/3 or 8:3
Therefore, ratio = 8:3 Answer.

Distance Upstream = Distance Downstream.

Speed Upstream * Time Upstream = Speed Downstream * Time Downstream.
(x - y) * 44/5 = (x + y) * 4,
24x = 64y,
x:y = 8:3.

Thanks for this short trick @Mahesh.