Aptitude - Boats and Streams - Discussion

@Rohit.

Perfect explanation, Thanks.

Let stream is considered as "S"

Speed Downstream = (10+S).
Speed Upstream =(10-S).

Upstream Speed - Downstream Speed = 90/60 (minutes converted to hour).

36/(10-S) - 36(10+S) = 90/60.

36(10+S) - 36(10-S) / (10+S) (10-S) = 3/2 ( Divided those) {(10+S) and (10-S) as LCM}.

360+36S-360+36S / 100-10S+10S-S^2= 3/2 (360 and 10s Subtracted).

72S / (100-S^2) = 3/2.

144S = 300 - 3S^2 (cross Multiplication).

3S^2 + 144S - 300 = 0.
S^2 + 48S - 100 = 0 (ALL are divided by 3).

S^2 + 50S - 2S -100 =0.
S( S+50) - 2(S+50) = 0.
(S+50) (S-2) = 0.

S = - 50 (Is not granted).
S = 2.

So the speed of the stream is 2.

x = 10.
36/(10-x) - 36/(10+x) = 90/60,
36/(10-x) - 36/(10-x) = 3/2.
then 12*4 = 36.
divide all no. * 12.

12/(10-x) - 12/(10-x) = 1/2.
(12/(x-y)- 12/(x+y)) / ((10-x)(10+x)) = 1/2.

Multiply by * 2 all equation.
24(10-x) - 24(10+x) = (10-x)(10+x),
240 + 24x - 240+ 24x = (10-x)(10+x),
24x + 24x = (10-x)(10+x),
48x = 100+10x-10x-x^2,
48x = 100- x^2,
48 = 100-x,
x= (100/48),
x = 2.

In question time taken is 90 min less. How you can add or substrate time data with speed? Please tell me.

Why are we subtracting downstream and upstream? Please explain.

36(10 + x) - 36(10 - x) = 90\60.

How to solve this?

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.

Let the speed of the stream be x mph.

Then sp. Downstream=(10+x) mph.

Sp. Upstream =(10-x) mph.
(36/10-x) - (36/10-x) =90/60.

Can be written as (36/10-x)- (36/10-x) = 9/6,

[360+36x-360+36x]6 = 9(10^2-x^2),

72x * 6= 900-9x^2,
9x^2+432x-900=0,
x^2 +48x -100=0.
(x+50)(x-2),
X=2mph.

Let upstream time be T hrs.
Then, downstream time will be T-3/2 hrs.
Upstream - downstream = T - T + 3/2 = 3/2 hrs = 90 minutes.

Hi, I am unable to understand this step that is 72X x 60 =90(100 - X^2).
X^2 +48X - 100 = 0.
(X +50) (X - 2).
X=2mph.