Aptitude - Boats and Streams - Discussion

4. 

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

[A]. 4
[B]. 5
[C]. 6
[D]. 10

Answer: Option B

Explanation:

Let the speed of the stream be x km/hr. Then,

Speed downstream = (15 + x) km/hr,

Speed upstream = (15 - x) km/hr.

30 + 30 = 4 1
(15 + x) (15 - x) 2

900 = 9
225 - x2 2

9x2 = 225

x2 = 25

x = 5 km/hr.

Video Explanation: https://youtu.be/lMFnNB3YQOo


Rajesh Kumar said: (Feb 8, 2011)  
-x2+225=200
=>x2=25
=>x=5km/hr

Ezhil said: (Feb 24, 2011)  
Hai, Mr. Rajesh Kumar, can you explain me in brief?

John said: (Jul 8, 2011)  
How it is possible to multiply the speed of upstream and downstream?

Bhavani said: (Jul 18, 2011)  
Explain briefly.

Jyoti said: (Jul 31, 2011)  
Hello friends,

In this Speed of the boat in still water is given that is 15Km/s. and here we find speed of stream. take the answer from bottom suppose i take 10 from bottom.

You can see that speed of boat in upstream become15-10=5 and distance of upstream is 30 given. Here you can find out the time in case of upstream time=dist/speed 30/5=6.

Similarly speed in case of downstream 15+10=25. Distance 30 given time you can find that is=30/25=6/5. In question, we have given total time 4hr 30min. We can see that the answer 10 is choosen by me is wrong. Take 5 in place of 10 you get the answer.

Folake said: (Sep 8, 2011)  
I don't really understand this question. Some one should please help me out.

Vinoth said: (Sep 28, 2011)  
Simply follow formula when only distance the, time t and speed of boat x given.. and asked for speed of stream.... use in formula,

d^2/(x^2-y^2)=t ,

9/2=(225-y^2)/15, ==> y^2=25 , y=5

Seetha said: (Oct 7, 2011)  
Here we have been given the speed of the boat is 15 kmph that too in still water and the boat goes and comes back in 4 and half hour and that distance is 30 kms so we have to find the speed of the stream in kmph.
Let us think that the speed of the stream be X then
We know that Speed of the downstream is (u+v) here u is speed of the boat and v is speed of the stream so
Speed of downstream is (15+x)Kmph
Speed of upstream is (15-x)Kmph
We know that
speed in still water is 1/2(a+b) kmph
so
30/(15+x) + 30/(15-x) = 4 1/2

30*30/(15+x)(15-x) = 4 1/2 [Since we know (a+b)(a-b) = (a2 - b2)

900 / 225 - x2 = 9/2

cross multiply the two fractions

then 900 * 2 = 9(225 -x2)

1800 = 2025 - 9x2

9x2 = 2025-1800

9x2 = 225
x2 = 225/9
x2 = 25
x = 5

This is the solution

Riaan said: (Nov 3, 2011)  
What dou mean by still water?

Rohit Chavan said: (Nov 21, 2011)  
Total time=(distance of downstream/speed of downstream)+(distance of downstream/speed of downstream)

Therefore, (30/(15+x))+(30/(15-x)) = 9/2 hrs

Then find the value of x by simplifying the above equation.

Sunil Sharma, Kaverinagar said: (Mar 21, 2012)  
How can you multiply in place of addition ?

Varun said: (May 19, 2012)  
Here only one direction distance is given. Time which requires to go and back position is given. How is possible to put total time to only one direction distance.

Jagu said: (Jun 15, 2012)  
How we get 9/2 there please tell me.

Neha said: (Aug 18, 2012)  
By solving the fraction 4*2=8, n 8+1=9, so the ans is 9/2

Sourabh said: (Aug 19, 2012)  
Very well Explained Seetha ...Thank you.....

Abhishek said: (Oct 12, 2012)  
Thank You...!

Seetha

Arun.D said: (Jun 3, 2013)  
Speed in still water = 15 km/hr.
Distance traveled in downstream = 30 km.

Time taken in upstream = 4 hr 30 min.
The speed of the stream = ?

Speed = Distance/time.
Distance = 30km.

Speed in upstream = (u-v)km/hr = (15-v)km/hr.

Speed in downstream = (u+v)km/hr = (15+v)km/hr.

Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).

(30/(15+v))+(30/(15-v)) = 4 1/2.

(30*30/(15-v)(15+v)) = 4 1/2.

900/(15^2 - v^2) = 4 1/2.

900/(225 - v^2) = 4 1/2.

900 / (225 - v^2) = 9/2.

900 * 2 = 9(225 -v^2).

1800 = 2025 - 9v^2.

9v^2 = 2025 - 1800.

9v^2 = 225.

v^2 = 225/9.

v^2 = 25.

v = 5 Km/hr.

Mohanraj said: (Jun 17, 2013)  
Friends this step is little confused any can help please?

(30/(15+v))+(30/(15-v)) = 4 1/2.

(30*30/(15-v)(15+v)) = 4 1/2.

Asha said: (Jun 23, 2013)  
How can calculate distance of upstream ?

Vinay said: (Jul 11, 2013)  
How can calculate distance of upstream ?

Kavitha said: (Sep 6, 2013)  
The distance in both down&upstream is 30 as given;.

Here we have to find the speed. So distance/speed=time.

(30/15+x) + (30/15-x) = 4 1/2 = 9/2(2X4+1/2 = 9/2).

By solving it we get the answer.

Asirbad said: (Jul 20, 2014)  
Actually all of them are wrong who are saying that the answer would be 5.

Because the first step itself is wrong.

If a man covers a certain distance at x km/hr and returns at y km/hr then the avg speed is 2xy/(x+y). I think you all know this.

So the first step will be,

2(15+x)(15-x)/(225-x2) = (30)/(4.5).

Guys think about it.

Varun said: (Oct 24, 2014)  
How there 41/2 will came?

Ajax said: (Nov 27, 2014)  
Simple to find speed of stream to check option.

A) 4.
= 15+4/2 + 15-4/2.
= 4.25 hr so wrong.

B) 5.
= 15+5/2 + 15-5/2.
= 4.5 hr so right answer.

Smruthi said: (Dec 9, 2014)  
What is the difference between 4 sum and 8 sum having the same description?

Rajesh said: (Jan 30, 2015)  
How we will getting 30 sir?

Farman said: (Feb 10, 2015)  
See its simple to understand.

Given distance is 30km. Let assume speed of river is x.

Speed of boat is 15 once it goes downstream. So speed would be 15+x.

And upstream is 15-x.

Now what it told from going to 30 km time required would be 30/downstream and coming back speed would be 30/upstream.

So total time given here is 4.30 minutes which is 4*1/2 (1/2 here means 30 minutes which is half of 1 hr).

So adding both the times downstream and upstream would give total time which is 4*1/2.

i.e why its gives 30/(downstream speed)+30/(upstream) = 4*1/2.

And now you are smart enough to solve equations.

Owen said: (Mar 30, 2015)  
What confuses me is that I expected the time gained going down to be same as that lost going up.

Finding the velocities etc easy way to solve this, but I still find the thought difficult to get around that whatever the stream gives in time going down should be lost going back But its just not true!

John said: (Jul 20, 2015)  
What happen to the 900 and the 2?

Sagar said: (Aug 16, 2015)  
In a stream running at 2km/h, a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the motorboat in still water? Please answer.

Lakki said: (Aug 31, 2015)  
Any shortcut method for this sum?

Aary said: (Sep 10, 2015)  
How did we get 30*30 = 900?

Are we taking 30 common or what?

Roneet Jena said: (Dec 5, 2015)  
[(450-30x)+(450+30x)]/(225-x^2) = [900/(225-x^2)].

Adityalath said: (Jan 2, 2016)  
Short trick:

D = z(x^2-y^2)/2x.

Where.

D = Distance.

Z = Time taken.

x = Speed of boat in still water.

y = Speed of stream.

30 = 9*(15^2-y^2)/2*2*15.
200 = 225-y^2.

y^2 = 25.
y = 5 answer.

Sneha said: (May 27, 2016)  
How you people got 9/2? Please explain that.

Anjali said: (Jun 24, 2016)  
Please explain it in an easy way, which will be helpful for me.

Ranjith said: (Aug 28, 2016)  
4 hours and 30 minutes as 9/2. Total in terms of km/ hr.

Muthu said: (Sep 23, 2016)  
@Ajax.

You answer is very simple. But I don't understand it please explain Clearly.

Eve said: (Sep 30, 2016)  
Why is it downstream + something and upstream - something?

Shubh said: (Nov 2, 2016)  
Agree @Arun D.

Prabhat said: (Nov 11, 2016)  
Whoever is having confusion about how it got multiplied in place of addition in
(30/(15+x)) + (30/(15-x)) = 9/2 hrs.

It is by cross multiplication it will become,
(30 * (15-x))+(30 * (15+x)) / (15+x) * (15-x) = 9/2 hrs.

After simplifying it will become 900/15^2 - x^2 = 9/2.

P Dixit said: (Dec 3, 2016)  
Put in Formula.

If total Distance = D= 30, Total Time = T= 9/2 Hr., Boat Speed= B = 30, Stream Speed = S=?,

Then,
Distance between the two places is D = T(B^2 - S^2)/2B
S = 5 Ans.

Darshana Jain said: (Feb 16, 2017)  
Thank you very much for the given explanation.

Srinivas said: (Mar 1, 2017)  
Nice explanation @Seetha.

Krishna said: (Mar 22, 2017)  
The answer is 4 * 1/2 = 2.

How is it possible the answer is 9/2. If 4+1/2 then only answer is 9/2.

Rohit said: (Apr 2, 2017)  
How came 4(1/2)?

Praveenbehera said: (Apr 26, 2017)  
Good explanation @Seetha. Thanks.

Priya said: (Jul 11, 2017)  
The speed of the current is 5 then the speed of the boat in downstream =u+v =15+5 =20;.
The speed of the boat in upstream = u-v = 15-5 =10;.
Time =distance/speed.
4 1/2 = 30/20+30/10.
9/2=9/2.

Pawan Thakur said: (Sep 10, 2017)  
Sneha just like that 4 hours 30 minutes.

Convert 30 minutes 30/60 you will get 1/2.
Now 4 hours 30 minutes = 4*1/2 you will get 9/2 in place of 30 minutes put 1/2.

Sowmya.G said: (Oct 1, 2017)  
Speed= 15km/hr
Distance= 30 km/hr
Time= distance/speed
Speed of stream (v) is taken as x
Speed of boat in still water(u)=15km/hr
So,
Speed upstream=(15-x) km/hr.
Speed downstream=(15+x)km/hr.

30/15+x + 30/15-x=4 1/2(this is equation is written with the help of, time= distance/speed)
Further calculations are made. So we get x=5 km/hr.

Gourav Shervegar said: (Nov 22, 2017)  
Why the speed of upstream is 15-x and speed of downstream is 15+x?

Breetha said: (Nov 24, 2017)  
A little confusion in simplification. How 900 came? Explain.

Sai said: (Jul 25, 2018)  
We know that.

Still in water + stream = downstream.

In question downstream distance and time is given, we get the downstream speed and still in water speed also given.

Then we can find the stream speed easily.

Geetha said: (Sep 10, 2018)  
How 900 came? Explain.

Disha said: (Sep 18, 2018)  
@All.

x=consider speed of boat , which is 15kmph.
d=30km.
t=4hr30 min.

Given in question that it comes back, means the boat has taken a lap .so it will be one time upstream and second downstream. That is why both x+y and x-y has been taken.
30/(x+y)+30/(x-y)=9/2.
x=5.

Basavaraju H K said: (Oct 23, 2018)  
30/(15+x)+30/(15-x)=4 1/2.

Don't multiply take LCM then it will be;

{ 30(15- x)+30(15+x)}/(15+x)(15-x) = 4 1/2.
450-30x+450+30x /(15+x) (15 - x) = 9/2.
-30x+30x will be cancelled then;
900 /15^2-x^2=9/2.
**(a+b)(a-b)=a^2-b^2 **

When cross multiplied we get;
2 * 900=9(15^2-x^2),
1800=2025-9x^2 so,
9x^2=2025-1800,
9x^2=225,
x^2=225/9,
x^2=25,
x = 5.

Monika said: (Oct 25, 2018)  
Thank you all for giving the answer.

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