Aptitude - Boats and Streams - Discussion

Please give me any shortcuts to find the solution.

Well done @Sowmya.

Yes. So option A is correct.

We know,
Distance = Time x Speed.

Distance is same for both up and down streams => d = 36.
Speed of boat in still water is 10 => u = 10.

Let time for up stream be "t" and time for down stream becomes "t-(90/60)".

We need to find speed of the stream i.e; v = ? (say x).

From distance = Time x Speed => Time = Distance/Speed.

So, time for up stream t = 36/(10 - x) and,
Time for down stream (t - (90/60)) = 36/(10 + x).

For above to get 'x' value we need to subtract time for upstream and time for downstream.

=> t - (t - (90/60)) = [36/(10 - x)] - [36/(10 + x)].
=> 90/60 = 36{[1/(10 - x)] - [1/(10 + x)]}.
=> 90/60 = 36{ [(10 + x) - (10-x)]/[(10*10) - (x*x)]}.
=> 1/2 = 12 {[2x]/[100 - x2]}.
=> 100 - x2 = 12 * 2 * 2x.
=> 100 - x2 = 48x.
=> x2 + 48x - 100 = 0.

And here we got the complete equation with one variable "x" that is what we need to find so we can simply substitute options and check.

From the Option [A] will fit the above equation.

Super @Sowmya. Your explanation is an easy way to get the answer.

Please tell me 1 mile = ?

Shortcut:

Distance D = 36.

Time T = 90 minutes.

90 minutes = 1.30 hrs.

D = S/T.

36 = S/1.3.

S = 2.

Miles per hour.

Mph means what? "Miles per hr or meter per hr".

@Rohit.

Distance/Speed = Time.

Taking x as speed of the stream.

Upstream distance/(Still_water_speed - x) or Upstream time minus Downstream_distance/(Still_water_speed - x) or Downstream time.

Equals to 90 mins/60 dividing by 60 as we want to bring all the time values to the same unit.

This thing is already mentioned in the problem.

"A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream".