Aptitude - Boats and Streams - Discussion

Just look simple method:

Upward= 8 hr + 48 Min. = 8+48/60 = 44/5.
Downward = 4 hr.
Speed of stream = (44/5 -4)/2 = 2.4 hr.
Speed of boat = 4+2.4 = 6.4 hr.
So, Ratio is 6.4:2.4.
i.e 8:3.

Let,

Upstream speed = X kmph.
Downstream spead = Y kmph.

So,
We know that distance is the same.
And we know, D=SXT (speedxtime)
D= X(8+48/60) upstream case--->eq1
D=Y(4)---> eq 2
Now, equate both.

4Y = X(8+4/5).
4Y= X(44/5).
Y=X(11/5).
Y/X = 11/5.

So now relate as Y=11, X=5.
Now speed of water(S.W) = downstrean-upstream/2.
= Y-X/2.
=11-5/2 = 6/2 = 3.

Now, speed of boat = downstream - speed of the water.
= Y- (S.W).
= 11-3 = 8.

Now ratio of both as given in question,
Ratio of boat speed to water speed = 8/3.
Ratio = 8:3.
Hope you'll get it well.

Thank you. @Tushar Pawar.

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.

Well said, Thank you @Mahesh.

@All.

You did not mention which speed of the boat to be calculated if it was in the still water or downstream or against the stream!

By using the formula we have;
Speed upstream = u-v.
Speed downstream= u+v.
Where u&v is speed of the boat in still water and speed of stream respectively.
Given that distance covered is equal so;

By the time distance formula;
Speed *time= distance.
Both the values put according to formula.
(u-v) *8*48/60=(u+v) 4.
(u-v) 8*4/5=(u+v) 4.
44/5u-44/5v= 4u+4v.
44/5u- 4u = 44/5v+4v.
u[44/5-4] = v[44/5+4].
24u = 64v.
u/v = 64/24.
u/v = 8/3.

So, the ratio between the speed of the boat and speed of the water current is;
8:3.

Assume distance as 100 km.

Calculate Speed @ downstream (100/4hrs) = 25 km/h
Calculate speed @ upstream ( 100/ 8.8 hrs) = 11.36 km/h
Take the difference of both and divide by 2 to get the speed of the river.
(13.64/2)= 6.82 km/h.

To calculate the speed of the boat minus the speed of the river, from speed @ downstream (25-6.82) = 18.18 km/h.
Now as you have both speeds, calculate the ratio (18.18/6.82) = 2.66 = 8/3.

How this required ratio? pls explain?

Let the speed of the Boat be X kmph and Speed of the stream be Y kmph.

Then 44/5 * (X-Y) = 4 * (X+Y).

By solving the equation you will get X/Y = 8:3.

I hope you'll understand.