Aptitude - Boats and Streams - Discussion

The ratio between time in downstream to upstream is 1:3/2 = 2:3, then the ratio between speed is 2 : 3(directly proportional).
The difference between the ratio is 1 and is given as 3.
The speed of still water is x+y that is (2+3)×3 = 15.

@All.

By checking the options we can find the answer.

Time has already been given in the question. And these options are the speed of the boat in still water.

And you know the rate of current as well. Just check which option gives you the same distance upstream as well as downstream (D=S*T).

Why we have not taken total time as 5/2? Please explain it.

If Time=Distance/Speed.

Speed=Distance*Time.

According to condition distance of D.S and U.S is same.
D.S=U.S.
(x+3)*1=(x-3)*3/2 {Remember S=D*T.}.
{i.e D.S and U.S distance which is x+3 and x-3 respectively} and {D.S and U.S time which is 1 and 1*1/2=3/2 respectively}

2x+6=3x-9 (Multiply both equations by 2 to get rid of denominator 2 and solve).
6+9=3x-2x.
x=15.

I have one more way to solve it...

The boat goes downstream in 1 hour and returns back in 3/2 hours so we can conclude the boat covered the same distance.

Now, Sb = 1/2(Sd+Su)
Sb = 1/2(D/1 +D*2/3). As speed = Dist./Time
Sb = D(1/2+1/3)
Sb = D((5/6) -------> (1)

Also, Ss = 1/2(Sd-Su)
Ss = 1/2(D/1-D*2/3)
Ss = D(1/2-1/3)
Ss = D(1/6) -------> (2)

Now if we take ratio of (1) & (2) then,
Sb/Ss = [D(5/6)]/[D(1/6)].
Sb/3 = 5.
As speed of stream is 3kmph.
Sb = 15 kmph.

Here Sb is the speed of the boat.
Ss is the speed of the stream.
Sd is the speed of downstream.
Su is the speed of upstream.
D is distance.

Yes, you are right. @Syed.

But we find only the distance. But the question asked is the speed of the boat in still water.

Can anyone explain this?

Yes, right @Suraj Dev.

The speed of the boat in still water formula is 1/2(a-b) right then why there is no usage of formula here.

Why we taken x-3 why can't 3-x?

Please explain me.

But in question, there is still water mention not, the velocity of the boat in "still water" needs to be found not in downstream.