Aptitude - Boats and Streams - Discussion

15. 

A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

[A]. 1 km/hr
[B]. 1.5 km/hr
[C]. 2 km/hr
[D]. 2.5 km/hr

Answer: Option A

Explanation:

Suppose he move 4 km downstream in x hours. Then,

Speed downstream = 4 km/hr.
x

Speed upstream = 3 km/hr.
x

48 + 48 = 14 or x = 1 .
(4/x) (3/x) 2

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream = 1 (8 - 6) km/hr = 1 km/hr.
2


Rajesh said: (Jan 13, 2011)  
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

How we know these values 8 km/hr, 6 km/hr..

Pls tell me.

Ram said: (Jan 31, 2011)  
I'm also having this doubt. Anybody help me.

Manish said: (Feb 6, 2011)  
Speed of down stream is always greater than upstream because in down stream the gravitational force enhence some speed of the stream.

Manish said: (Feb 6, 2011)  
We know that x=1/2, put this value in speed downstream= (4/x) then we get speed down stream=8km/h similarly we get speed upstream.

Rohit said: (Jul 30, 2011)  
Is there any other solotion without assuming the x ?

Anik said: (Aug 15, 2011)  
@Rohit

It is impossible without assuming x i.e algebraic method, learn more on this.

Faiz said: (Jun 17, 2012)  
Let speed in still water be s.

Let speed of stream be x.

So, 48/ (s+x) +48/ (s-x) =14 - First equation.

and

4/ (s+x) =3/ (s-x) - Second equation.

Solving the above two equations,

We get,

X=1, Which is the answer.

Jain said: (Sep 2, 2013)  
Let overall speed be 'v'.

And speed of stream be 'x'.

v = (48+48)/14 = 7.

And 4/(v+x)=3/(v-x) given.

Put the value of 'v' in above eq. and find 'x'.

Usamah said: (Sep 22, 2013)  
Explain me last step. 1/2(8-6) = 1 km/hr which is rate of stream.

Sean Simbota said: (Jan 13, 2014)  
@Usamah.

If the speed downstream is Akm/hr and the speed upstream is Bkm/hr then;
Rate of stream = 1/2(A-B)km/hr.
Therefore;1/2(8-6).
= 1/2(2).
= 1 answer.

Rushi said: (Feb 2, 2014)  
At his usual rowing rate rahul can travel 12 mile downstream in a river in six he less than it takes him to travel the same distance upstream. But if he could doubled his usual speed for 24 miles round trip, the downstream 12 miles would then take only one he less than the upstar. 12 miles. Find current rate per hr?

Vishwas said: (Feb 15, 2014)  
Don't break your head.
Just follow this:

Assume that he moves 4 km downstream in x hours.

Then, speed downstream = distancetime=4x km/hr.

Given that he can row 4 km with the stream in the same time as 3 km against the stream.

i.e., speed upstream = 34of speed downstream=> speed upstream = 3x km/hr.

He rows to a place 48 km distant and come back in 14 hours.

=>48/(4x)+48/(3x)=14==>12x+16x=14=>6x+8x=7=>14x=7=>x=12Hence, speed downstream = 4x=4(12) = 8 km/hrspeed upstream = 3x=3(12) = 6 km/hr.

Now we can use the below formula to find the rate of the stream.

Padma said: (Apr 7, 2014)  
I am not able to understand why x=1/2 and,
Speed downstream = (4/x).
Speed upstream = (3/x).

Can anyone clear my doubt?

Mahesh said: (Jul 6, 2014)  
@Jain.

How come v = (48+48)/14 = 7.
The ans is 6.857.

Have you taken it approximately.

Ashwini Singh said: (Aug 19, 2014)  
Suppose the time taken in downstream be x hour.
distance of downstream = 4km(given).

So speed in downstream = distance/time = 4/x ------(1)

Now according to question same time he is taking for upstream.
so Speed of upstream = 3/x ----------(2).

Now total time given is 14 hours.

According to question:

Time taken by upstream + time taken in downstream = 14 hours.

48/(3/x)+ 48/(4+x) = 14.
Solving this we get x = 1/2.

Now putting this value in equations 1 and 2 we get;

Speed of upstream = 6 km/h.
Speed of downstream = 8km/h.

Now rate of stream = 1/2(Speed of downstream-Speed of upstream).

i.e 1/2(8-6) = 1km/h.

Adi said: (Sep 30, 2014)  
My doubt is:
Is he rowing alternatively first 4 km downstream then 3 km upstream so he will cover 28 km @ 4km/hr and 20 @ 3km/hr (kind of work and time example 2 people working on alternate day with different capacity).

Tamilazhagan said: (Oct 9, 2014)  
Some body says why = 1/2. Solution is 48/(4/x)+48/(3/x) = 14.
Now 48x/4+48x/3 = 14.

Take x as common x(48/4+48/3) = 14.
Then x(12+16) = 14.

28x = 14.
x = 12.

Pankaj said: (Apr 10, 2015)  
Hope this method will help you guys.

Speed of boat: B km/h;
Speed of stream: S/km/h;

So Downstream Speed (with the stream) = Speed of boat + Speed of stream;

Upstream Speed (against the stream) = Speed of boat - Speed of stream;

Downstream speed = (B+S) km/h;
Upstream Speed = (B-S) km/h;
Total Distant = 48 km;

Since in question, it is given that time taken by a man to travel 4 km with stream (B+S) is equal to time taken to travel 3 km in against direction (B-S).

Or

4 km with (B+S) km/h = 3 km with (B-S) km/h.

4/(B+S) = 3/(B-S);
4B-4S = 3B+3S;
B = 7S;
B/S = 7/1;

So Boat speed = 7x;
Stream Speed = x;

Now using question first line:

A man rows to a place 48 km distant and come back in 14 hours.
Time taken to travel down stream + time taken to travel upstream = 14;

= 48/(7x+x) + 48/(7x-x) =14;
= 6/x + 8/x = 14;
x = 1;

So boat speed = 7*x = 7*1 = 7km/h;
Stream speed = x = 1 km/h;

Thanks.

Rishi said: (Jun 2, 2015)  
Let rate of stream and still water be v km/hr and u km/hr respectively.

So speed in downstream = u+v km/hr.

Speed in upstream = u-v km/hr.

In question distance traveled in both direction is same = 48 Km.

So 4/u+v = 4/u-v.

=> u/v = 7/1.

Now we can say u = 7k & v = k.

So time of downstream = 48/8k = 6/k and time in upstream = 48/6k = 8/k.

Now from question time up + time down = 14hr.

So (8/k)+(6/k) = 14 => k = 1. So u = 7 km/h.

And v = 1 km/h answer.

Aparna said: (Jul 16, 2015)  
How did you got that x=12 I think x=7/14 so x=1/2?

Can you explain me is it right are wrong please?

Chirag Gupta said: (Aug 11, 2015)  
Why we divide this by x?

I think answer should be 2 km/hr.

Pulak Sarkar said: (Mar 10, 2016)  
Downstream 4/x = 4/1/2 = 4*2 = 8kmph.

Upstream 3/x = 3/1/2 = 3*2 = 6kmph.

Kiran said: (Apr 29, 2016)  
This can also be solved using Avg speed concept.

Let t be time taken.
Let x be stream speed & v be boat speed.

Total distance = 48 + 48 = 96.
Time = 14 hrs.

So, 96/14 = 2ab/(a+b) = 2((4/t*3/t)).
==> 7/t.

Solving we get t = 1/2 hr.
=> 4/(1/2) = 8.
=> 3/(1/2) = 6.
So, v+x = 8 & v - x =6.
Solving we get v=7 : x=1.
Stream speed = 1/2 (8 - 6) = 1 km/hr.

Max said: (May 17, 2016)  
A man can row 24 km upstream and 54 km downstream in 6 hours. He can also row 36 km upstream and 48 km downstream in 8 hours. What is the speed of the man in still water?

Nessa said: (Dec 8, 2016)  
How did you get x = 1/2? I got it as 2.

Pouvanam said: (Feb 14, 2017)  
How do you find the value of x?

Priya said: (Mar 13, 2017)  
Distance=48 km in 14 hours.
rate of stream = x.
downstream=4 km (with the water).
Upstream =3 km(against the water).
Rate of the stream =1/2(4-3)=1/2.
Therefore x=1/2.
Then,4/1/2 =4 * 2 = 8.
Then,3/1/2 = 3 * 2 = 6.
So,1/2(8-6) = 1/2(2)

Answer is 1.

Shanur Rahman said: (Jun 26, 2017)  
Suppose it took him x hrs to go downstream, then it will take him 14-x upstream. Therefore x/ (14-x) = 3/4.

There you go.

Subhrasubha Priyadarsini said: (Jan 11, 2018)  
4/x+y=3/x-y,
4x-4y=3x+,
x=7y -----> eq1
48/x+y +48/x-y =14,
48/8y+48/6y=14,
14/y=14,
y=1,
Now x=7.

Divya said: (Jan 16, 2018)  
Given : 4/x+y = 3/x-y --> (1).
by solving the eq > x =7y.

and : 48/x-y + 48/x+y = 14.
48//7y-y + 48/7y+y = 14.
48/6y + 48/8y = 14.
8 + 6 =14y,
14 =14y,
y = 1km/hr.

Elvis said: (Mar 5, 2018)  
Given :
Distance downstream: Da= 48km (rowing along the stream)
Distance upstream: Db= 48km (rowing against the stream)
Total time for going and coming back i.e 1st going along the stream and then against the stream :
Ta+Tb= 14 h
Relation between upstream and downstream given in variable:
Downstream Distance, da = 3 km
Upstream Distance, db = 4km
Let, u = speed in still water in kmph & v= speed of stream kmph
Formula
downstream speed = (u+v)kmph &
uspstream speed = (u-v)kmph
We know , time =dist/speed

Solving for given relation
hence, time for upstream=upstream dist/upstream speed
tb = db/(u-v)
tb = 3/(u-v)
time for downstream=downstream dist/downstream speed
ta = da/(u+v)
ta = 4/(u+v)

But its given ta=tb.
hence 3/(u-v)=4/(u+v)
u=7v.

Relation solved*

Now since, Ta+Tb=14 , i.e time for downstream in 48 km + time for upstream in 48 km
again time =dist/speed
Ta = 48/(u+v)
Tb = 48/(u-v)

Ta + Tb = 14
48/(u+v)+48/(u-v)=14
solving you will get,
48v2-48v=0 i.e 48v(v-1)=0
Hence 48v=0 and v-1=0,
Therefore v=0 or v=1.
But v can not be 0kmph hence v = 1 kmph.

Rya said: (Jul 6, 2018)  
Total distance is 48 that means he travels 24km downstream and 24km upstream, why we are taking the whole 48km to calculate the separate down and upstream time? Please tell me.

Surya said: (Nov 25, 2018)  
the speed of an up stream=x+y/2;
the speed of a down stream=x-y/2;
So they have given like 4km with the stream and 3km against the stream so
x+y/2=4;

x+y=8------------(1);
x-y=6-------------(2);
---------
2y=2;
-----------
y=1 rate of stream;

Mandal Shuvo said: (May 22, 2019)  
Let rate upstream be x and downstream be x/2 then required ratio be 3x/4:x/4 = 3 : 1 is answer.

Patchala.Lokesh said: (Oct 6, 2019)  
Very simple it takes 3km/hr to travel down stream and 4km/hr to travel upstream so the difference b/w 4-3=1 is the rate of stream.

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