Aptitude - Boats and Streams - Discussion

Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.

T = 1hr.
total time = (downstream speed/speed of downstream)+(distance of upstream/speed of Upstream).

we don't know distance so let it be 'x'
so, 1 = x/6 + x/4.
take lcm and do eqaution u will get
2x + 3x = 12,
5x = 12,
x = 2.4 km.

Boat => 5.
Water => 1
Downstream = 5+1 = 6.
Upstream = 5-1 = 4.

D = T*S
D = 1 * (6)(4)/10.
Then D. = 2.4.

Here Speed = Product of two speeds/ Sum of two speeds.

@Bhima,

You need to find out the L.C.M of the denominators. We multiply the denominator when L.C.M is not possible.

I solve this question and I got a different answer i.e. 10 km is the distance.

Upstream speed = 5km/h - 1km/h = 4.
Downstream speed = 5km/h + 1km/h = 6.

Distance =( upstream Speed * time) + (downstream speed * time).
= 4 * 1 + 6 * 1.
=. 10.

Let the distance be X in km.

And speed formula is given by;
speed(or velocity)=distance/time taken.
Speed Upstream= (5-1)=4 kmph.
Speed downstream =(5+1)=6 kmph.
( given time taken to come back is 1hr.)

*Equating time take during Upstream and downstream to 1hour. ie
Time(up strm) +Time(dwn strm) =1---> Eq(1)
(time=distance *speed) so Eq(1)becomes.
X/6 + X/4 =1.
Taking lcm of 6&4 we get 12.
3x+2x=12.
5x=12.
So x=2.4km.

I think you guys got it. Correct me if I have done wrong.

@Bhima,

You need to find out the L.C.M of the denominators. We multiply the denominator when L.C.M is not possible.

(4x+6x)/(6*4) = 1.
4x+6x = 24.

10x = 24.
x = 24/10.
x = 2.4.

I hope You are all understand.

For Who don't understand how come 12, please refer the following.

x/6 + x/4 = 1
then cross multiply we get;
4x+6x/24 = 1,
24 move to another side we get ;
4x+6x = 24,
divided by 2 for simplify we get;
2x+3x = 12.

Easy way to solve this type of question is followed by a simple formula.
i.e
D = T[sb square - ss square]/2*sb.

sb means the speed of a boat.
ss means the speed of a stream.

How 2x+3x=12 comes?