Aptitude - Boats and Streams - Discussion

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.

@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!

When the same distance is mentioned in this type of question best shortcut is the sum:difference. Nothing but 12hr 48 min: 4hr 48min.

Other than change completely minutes. so 768min:288 min = 8:3

Speed = Distance/Time.
Downstream = (u-v) km/hr.
Upstream = (u+v) km/hr.

Converting time to mins gives;
8hrs. 48 mins = 528 mins.
4 hrs. = 240 mins.

Let, Distance travelled = x km.

Therefore,
u-v = x/528 ----> 1.
u+v = x/240 ----> 2.

On dividing 1/2.

Therefore, (u-v)/(u+v) = 240/528 = 10/22.
On solving u/v = 32/12 = 8/3.

Thank you everyone for explaining.

8*4/5 will give 44/5 only which is not equal to 8hr 48min.

Please someone explain it to me, how 8hr 48min, how it becomes 8*4/5?

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.

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.

Upstream, x = b(speed of boat) - w(speed of water).
Downstream, y = b + w.

Equalling both using distance.
(b+w) *44/5 = (b-w) * 4.
(b+w)*11/5 = (b-w),
11b+11w = 5b-5w.

6b = -16w(ignore negative sign).
b/w = 8/3.
So, b : w = 8 : 3.