Aptitude - Boats and Streams - Discussion

3. 

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

[A]. 2 : 1
[B]. 3 : 2
[C]. 8 : 3
[D]. Cannot be determined
[E]. None of these

Answer: Option C

Explanation:

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

x x 8 4 = (y x 4)
5

44 x =4y
5

y = 11 x.
5

Required ratio = y + x : y - x
2 2

   = 16x x 1 : 6x x 1
5 2 5 2

   = 8 : 3
5 5

   = 8 : 3.


Anish said: (Jan 11, 2011)  
How this required ratio? pls explain?

Pradeesh said: (Jan 19, 2011)  
How can the y-x/2 become the current ratio?

Saranya said: (Jan 23, 2011)  
Can you explain the process clearly?

Ashis said: (Feb 1, 2011)  
As it is given to find out the ratio of speed of boat to speed of water w.r.to still water that is how required ratio is calculated.

You can find out from important formulae option i.e.

1/2(y-x)/1/2(y+x)
where y=speed at downstrem
x=speed at upstream.

Ravi said: (Feb 23, 2011)  
I didn't understand how 8*4/5 will get.

Bharath said: (Feb 25, 2011)  
Given is 8 hr 48min so converting min to hr

We have 48/60=4/5

Phani said: (May 26, 2011)  
Thanks Ashis.

Anchal said: (Jun 6, 2011)  
I am not able to understand the required ratio. ? how it is related with the speed of boat to speed of water. ?

Gita said: (Jun 16, 2011)  
I'm not able understand the ratio?can you give brief explanation.

Binza said: (Jul 9, 2011)  
Speed=distance/time
therefore distance=speed*time.
let consider speed at upstream is "x" and at downstream is "y", then distance covered (upstream in 8 hrs 48 min)= x*8*4/5

here 8hours and 48minutes=8*48/60=8*4/5

and distance covererd (downstream in 4hours=y*4

to relate both these equation
from question ,we know that distance covered are same

therefore x*8*4/5 = y*4

y=11/(5*x)
we know that speed are different in down stream and upstream.
if both are in same direction
take difference(x-y)
if they are in opposite
take sum(x+y)

required ratio =(x+y)/2 : (x-y)/2 // here 2 is to take average.
then answer is 8:3

Navya said: (Jul 20, 2011)  
I got it. 8*5+4=44.

Fractions!

Raja said: (Jul 27, 2011)  
8hr48min we need to convert 8hr48min in terms of only hr because we are required to compare 8hr48min to 4hr....and in 4hr there are no unit of any min therefore we have to convert 8hr48min in only hr ok....and 8 is already given in hr....
so that we will convert only 48min in terms of hr
60min=1hr
1min=1/60
similarly...
60min=1hr
1min=1/60
48min=(1/60)*48=48/60hr

[8(48/60)]hr=8(4/5)=8*5+4=40+4=44

Prasanth said: (Aug 31, 2011)  
@Binza

your explantation is not correct. This is not train problem to take like that. Speed of boat supported by extra speed of water current when down stream and reduced in up stream.

Pankaj said: (Sep 7, 2011)  
@ prasanth
binza concept is correct,but i still does't understand the avg?????

Bindu said: (Sep 11, 2011)  
As distance is same formula will be upstream speed X time1 =downstream speed x time 2

Time 1 =8+4/5=44/5 hrs,time2=4 hrs

(U-V)*44/5=(U+V)*4
44U-44V=20U+20V
24U-64V=0
24U=64V
U/V=64/24
=8/3.

Amit Lamba said: (Sep 23, 2011)  
I got this trick

as y =speed of boat in downstream
so it ll be equal to = speed of boat + speed of water
x= speed of boat in upstream
so it ll = speed of boat - speed of water
so y +x/2 =(spd of boat)
simillerly y - x/2 =speed of water

So thats way they took this ratio.

Sangu said: (Oct 8, 2011)  
Its the ratio between speed of the upstream and speed of the down stream.

Formula is (a+b)/2:(a-b)/2.

See the formula you will get it.

Rakesh said: (Nov 11, 2011)  
@sangu
Thank u a lot..

Gautam said: (Dec 28, 2011)  
Let the man's rate upstream be U kmph and that downstream be V kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

[U*8*48/60] = [V*4] [BECAUSE 1 MINUTE=60SECONDS]
[U*8*4/5] = [4V]
[U*44/5] = [4V]
44/5 U = 4V

THEN, USE THE FORMULA-----If the speed of the boat in still water is U km/hr and the stream of the boat is V km/hr then.

speed downstream = (u+v)km/hr
speed up stream = (u+v)km/hr

so, our U= 44/5 COME AND V= 4 COME

NOW, [U+V]/[U-V]
[44/5+4] / [44/5-4]
[44+20] / [44-20]
64/24,
8/3,
8:3 ANS

Manojit said: (Feb 8, 2012)  
Thanks Bindu.

Nitin Gusain said: (Feb 18, 2012)  
Take it as in easy way
x= upstream speed
y= downstream speed
now we know that
upstream speed(x) = boat speed - stream speed
downstream speed(y) = boat speed + stream speed
so, x+y = 2*boat speed
x-y = 2*stream speed
so ratio of boat speed to stream speed is = (x+y)/(x-y)

Aag said: (Apr 5, 2012)  
I got 13:3 please help I'm not getting 8:3.

Srinu said: (Aug 26, 2012)  
I didn't understand how 8*4/5 will get.

Anbu said: (Sep 5, 2012)  
Bindu your answer is suitable for all this type of problems?

Anbu said: (Sep 5, 2012)  
@Bindu.

Your answer is suitable for all this type of problems?

Hema said: (Oct 18, 2012)  
I'm not understand this step 16/5*1/2 please help me.

Ashwini said: (Jun 10, 2013)  
@Nitin Gusain.

Thanks yaar. It's so simple calculation.

But X-Y = -2 (Stream speed) So instead of that,

Y-X = +2 (Stream speed).

Maneesh said: (Jun 23, 2013)  
Simply equal the speeds in downstream and upstream we get the ratio,

upstream:downstream.

(x+y)/2 = (x-y)/2

(x+y) = (x-y)

Given upstream and downstream speeds,
Means x(44/5)=y(4).

y = x(11/5)

(x+Y) = (x-Y)

16x/5 = 6x/5

8:3 answer

Sandeep said: (Aug 29, 2013)  
x/y = 5/11.

So, x=5 , y=11.

(x+y)/2 : (x-y)/2.

(11+5)/2 : (11-5)/2.

16/2 : 6/2.

8:3 answer.

Raju said: (Aug 29, 2013)  
I want to know how these equation is done?

16x/5 and 6x/5.

Vikas Verma said: (Dec 6, 2013)  
Let the speed of the Boat be X kmph and Speed of the stream be Y kmph.

Then 44/5 * (X-Y) = 4 * (X+Y).

By solving the equation you will get X/Y = 8:3.

I hope you'll understand.

Papesh Roul said: (Jan 21, 2014)  
Let the speed of the Boat be: a kmph and Speed of the stream be: b kmph.

Distance =44/5 * (a-b) = 4 * (a+b).

By this equation we will get a/b = 8:3.

Sujishnu Adhya said: (Feb 16, 2014)  
An easy way to solve.

Let speed of boat and water be x km/hr and y km/hr respectively.

Upstream = x-y km/hr.

Downstream = x+y km/hr.

ATQ,

[8+(48/60)](x-y) = 4(x+y)(SINCE DISTANCE IS EQUAL).

8+4/5(x-y) = 4x + 4y.

44/5 x - 44/5 y= 4x + 4y.

44/5x - 4x = 4y + 44/5 y.

24x = 64 y.

x/y = 64/24.

x/y = 16 / 6.

x/y = 8 / 3 (answer).

Aparna said: (May 28, 2014)  
We all know this basic rule of finding ratio which is:
x/y = a/b.

Further when we solve this, we get:
x+y/x-y = a+b/a-b .... equation (1).

Solution:

Let the boat's speed upstream be x & downstream be y.

Therefore,
According to the formula, Distance = Speed*Time.
We get for upstream, D= x*44/5.
& for downstream, D= x*4.

Now, in the question, it is given that the distance covered is same while going upstream and downstream.

Therefore,
x*44/5 = 4y.
x/y = 11/5 (satisfies the equation: x/y = a/b).

Now put this value of x/y in equation (1).

x+y/x-y = 11+5/11-5.
x+y/x-y = 16/6.
x+y/x-y = 8/3.

8:3 is the Answer.

Mady said: (Jun 12, 2014)  
Boat Speed In still water = u.
Stream Speed = v.
DS = u+v US = u-v.

Distance = (u+v)4 = (u-v)44/5 (rough : 8*48/60= 44/5).

so (u+v) = (u-v)11/5 (rough : canceled 4 & 44.. 11 times).

5(u+v) = (u-v)11.
5u+5v = 11u-11v.
5u-11u = -11v-5v.
-6u = -16v.

u/v = 16/6= 8/3 .

So 8:3.

Jessie said: (Dec 16, 2014)  
How does the upstream:downstream relates the ratio speed of the boat:speed of the water current as asked in question?

Arjun said: (Apr 7, 2015)  
@Jessie.

The stream of the boat is also influenced by the flow of the current, and moreover given here is with the relationship of the boat speed with the current.

Ganesha (Lecturer) said: (Apr 7, 2015)  
You are excellent @Aparna, @Mady you too. Both are right is solving this but we have to go still easier and a shortcut method to solve why because is we can't waste 10 mins for a single aptitude in the examinations, which may lead to shortage of time.

Great job appreciative but still try best don't settle for good.

Prahadee said: (Jul 24, 2015)  
I don't understand the ratio. Can anyone explain me?

Bhomi said: (Aug 11, 2015)  
Let x be the speed of boat in still water and why be the speed of stream.

Since distance covered is same in both the direction.

(x-y)*8.8 = (x+y)8.

By solving x/y = (4/1.5) i.e x:y = 8:3.

Dd Dd said: (Oct 6, 2015)  
If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water = (a+b)/2 km/hr.

Rate of stream = (a-b)/2 km/hr.

Vishnu said: (Oct 7, 2015)  
Given x+y = 8 hours 48 minutes = 44/5.

x-y = 4.

Speed of boat is ((44/5)+4)/2 = 8.

Speed of current is ((44/5)-4)/2 = 3.

So the answer is 8:3.

Raj Patel said: (Dec 31, 2015)  
I don't understand (x*8 4) = (y*4)5.

Debjani Nandy said: (Feb 28, 2016)  
Speed of the boat upstream = Speed of boat - Speed of stream.

Speed of stream = Speed of boat - Speed of the boat upstream--------- (1).

Speed of the boat downstream = Speed of boat + Speed of stream.

Speed of stream = Speed of the boat downstream - Speed of boat-------- (2).

Now, equating (1) & (2),

Speed of boat-speed of boat upstream = Speed of boat downstream - Speed of boat.

2 (Speed of boat) = Speed upstream + Speed downstream.

Speed of boat = (Speed upstream + Speed downstream)/2.

If, Speed upstream = x and Speed downstream = y then,

Speed of boat = (x+y)/2.

Similarly, making speed of the boat as subject in eq (1) & (2) and then equating we get,

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

= (y-x) /2.

Rishikesh Agrawani said: (Apr 12, 2016)  
Let as assume,

The speed of boat is : b km/hr.

The speed of the water is : w km/hr.

In downstream the relative speed of the boat is: d = (b + w) km/hr.

In upstream the relative speed of the boat is : u = (b - w) km/hr.

According to the question,

The distance covered in upstream = (b + w) *4 km.

The distance covered in downstream = (b - w) * (8 + 48/60) km.

As the distance covered by boat is same in both direction, Hence.

(b + w) *4 = (b - w) *8.8.

(b*8.8) - (b*4) = (w*4 + w*8.8).

b*4.8 = w*12.8.

b/w = 8/3.

Or b:w = 8:3.

Trupti Udapure said: (Apr 13, 2016)  
Assume speed of boat = x km/h.
Speed of current = y km/hr.
Downstream speed = u km/h = 4km/h.
Upstream speed = v km/h = 8 hr 48 mins.
=> 8 * 4/5 = 44/5 km/hr.

Speed = Distance/Time.
So,
Distance = speed * time.
Distance covered is same.

Upstream distance = Downstream distance.
(44/5)*v = 4*u
(11/5)*v = u..
11/5 = u/v.

So, from ratio
u = 11.
v = 5.

x = (u + v)/2 and y= (u - v)/2.

x/y = (u + v)/(u - v).
= (11 + 5)/(11 -5 ).
= 16/6.
= 8/3.

Ratio = 8:3.

Balaji said: (May 8, 2016)  
Let u= man speed & v= stream speed.

We know downstream =u + v & upstream = u - v.

Then,

u - v = 8 + (48/60) = 8.8 hrs for upstream.

u = v = 4hrs for down stream.

Solving we get 6.4/- 2.4 (neglect sign).

Now, 6.4/2.4 = 64/24 = 8/3.

So, the answer is 8:3.

Rajver said: (Aug 20, 2016)  
I did not understand anything. Please let me know the easy way for this?

Ranjith said: (Aug 28, 2016)  
Let me explain.

Ratio between the speed of the boat and speed of the water current is :

Average speed of upstream and downstream to the water current speed (downstream - upward stream velocity we get average water moving velocity).

Shubh said: (Sep 6, 2016)  
Does anyone have an easy way to solve the problem?

Naren said: (Oct 2, 2016)  
8 hours 48 minutes is equal to 8.8 hours but how will it be equal to 6.4 hours?

Dhakshinamoorthi S said: (Oct 12, 2016)  
Let me do according to concept wise,

Given upstream time = 8+48/60 = 44/5.
Given downstream time is 4 hr.
We know distance covered by upstream = distance covered by downstream.
Therefore, 44/5(x - y) = 4(x + y).
When you solve the above equation,
we get 24x = 64y.
i.e,x/y = 64/24 = 8/3 the ratio is 8:3 which is the answer.

Saurabh Gupta said: (Oct 20, 2016)  
Given explanation is quite difficult to understand. Let me explain you this in a simpler manner.

Distance is same during upstream and Downstream and Distance is equal to : Speed/Time.

So, time in downstream = 4 hours,
Time in upstream = 44/5 hours (8 hours 48mins).
Now let's assume x as the distance.
A as the downstream speed and B as the upstream speed.

Now write both (as the distance formula),

44/5 = x/B ---> equation 1.
4 = x/A ---> equation 2.

Solving these two equations we get,

44/20 = a/b ---> equation 3.

By equation 3, we can say that a = 44b/20

And we want to calculate u : v.
i.e 1/2(a + b) : 1/2(a - b),
i.e (a + b) : (a - b),
i.e 44b/20 + b : 44b/20 - b,
i.e 64b/20 : 24b/20,
i.e 64b : 24b,
i.e 8 : 3.

That's It. I know it's a bit lengthy But you would be able to calculate 3/4 of these steps orally.

Shaiksha said: (Oct 22, 2016)  
Here distance is constant so, speed inversely proportional to the time.
Time taken by the boat upstream : time taken by the boat downstream = 44/5 : 4
= 11:5.

Speed of upstream : Speed of downstream = 1/11 : 1/5 = 5 : 11.

Speed of boat in still water: speed Of stream= (speed of upstream+speed of downstream) /2 : (speed of upstream speed of downstream)/2.

Therefore, (11 + 5)/2 : (11 - 6)/2 = 16/2 : 6/2.
ie 8:3.

Yogesh said: (Nov 16, 2016)  
You are right @Bindu.

Gokul Chandra Upadhyay said: (Dec 15, 2016)  
Let x = speed of boat.
y = speed of stream.
t1= upstream time & t2 = downstrem time.

formula : x/y = (t1 + t2)/(t1 - t2).
{t1 = 8h 48m = 44/5h, t2 = 4h}
so, x/y = (44/5 + 4)/(44/5 - 4).

x/y = (44 + 20)/(44 - 20) = 64/24 = 8/3.

x:y = 8:3.

Rahul said: (Feb 17, 2017)  
But I got the answer 3:1.

Please help me to get the correct answer.

Bhaskar said: (Jun 23, 2017)  
Explain me, why are we taking x=1 before 16x/5*1/2?

Bhaskar said: (Jun 23, 2017)  
Required ratio =(x+y)/2 : (x-y)/2 // here 2 is to take average.

Please, Explain this.

Bhaskar said: (Jun 23, 2017)  
Required ratio = (x+y)/2 : (x-y)/2 // here 2 is to take average.
Explain this.

Hely said: (Jul 8, 2017)  
Boat speed=x,
Water speed=y then.

The upstream speed of boat=(x-y),
And downstream speed of boat=(x+y).

The distance of upstream =speed of downstream
so, distance=speed * time.

(x-y)*528 = (x+y)*240,
(x-y)*(11/5) = (x+y),
11x-11y = 5x+5y,
6x-16y = 0,
6x = 16y,
x/y = 16/6,
x/y = 8/3 (speed of boat/speed of water).

Saransh said: (Jul 10, 2017)  
@Amit Lamba.

Thank you, it was easy to understand.

Vino said: (Aug 17, 2017)  
This method is easy to understand. Thank you @Hely.

Praveen Kumar said: (Aug 21, 2017)  
I don't understand why the factor 1/2 comes at the last while calculating the speed of the boat in upstream and downstream { (x+y) /2: (x-y) /2}?

Sekhar said: (Aug 29, 2017)  
The speed of the boat = 1/2(up stream + downstream) speed of the current = 1/2(up stream - downstream).

converting 8 hours 48 minutes to minutes which is 528 minutes.

converting 4 hours to minutes which is 240 minutes.

1/2(528+240) : 1/2(528-240).

1/2 on both sides gets canceled so,

768 : 288 ==> 8: 3.

Ramya said: (Sep 27, 2017)  
Could you please explain 2nd part of the answer (ratio) ?

Siddharth said: (Nov 9, 2017)  
It's very easy and understandable method. Thank you very much for this solution BINDU.

Manikandan said: (Nov 23, 2017)  
For required ratio:

The speed of boat:speed of current.
(u+v)/2 : (u-v)/2.
Here:y=11x/5 =u,
(11x/5+x)/2:(11x/5-x) //take LCM,
16x/5:6x/5,
16x:6x,
8:3.

Sriteja said: (Dec 9, 2017)  
@Sujishnu Adhya & @Binza.

Your explanation made me easy to understand. Thanks.

Deena.R said: (May 2, 2018)  
How ll can the 48/60 =4/5? Please explain why?

Dhiraj Take said: (May 11, 2018)  
@Deena R:.

Divide numerator and denominatr by 12.

Pratiksha said: (Jun 15, 2018)  
How that 8:3 ratio comes? Please anyone help me.

Hari said: (Jul 4, 2018)  
Anyone explain me to get the answer.

Ronie said: (Jul 28, 2018)  
First convert Hours to Mins.
8hrs 48mins= 528mins & 4hrs= 240mins.

Speed Down =x/528,
Speed Up=x/240,
Speed of stream =(x/240-x/528)÷2=x/880,
Speed of boat= x/240-x/880 =x/330,

Ratio=(x/330)/(x/880)= 8:3.

Ramjan said: (Sep 5, 2018)  
I got the value of x+y/2 =13x4 instead of 16x/10.

Am I correct?

Sagor said: (Nov 6, 2018)  
Let, the distance be = d.
Downsream speed= d/4,
Upstream speed= 5d/44,
So, d/4 : 5d/44.
11: 5.
Now, the speed of the boat =(11+5)/2.
= 8.
The speed of the current =(11-5)/2.
= 3.
So, ratio 8:3.

Pavan Chennur said: (Nov 7, 2018)  
Distance is constant. So that we have a relationship between speed and time.

Swapna said: (Dec 10, 2018)  
Thank you @Bindu.

Shivam said: (Mar 12, 2019)  
The speed of the boat in still water = Vb.
The speed of stream = Vs.

Question asked -- ratio, Vb : Vs = ?..

Vb + Vs = Vr1 (resultant speed downstream), and time taken to cover a distance "d" with speed Vr1 is 4 hrs.

Similarly,
Vb - Vs = Vr2 (resultant speed upstream), and time is taken to cover the same distance with speed Vr2 is 8 hrs, 48min.
By adding both the equations , we get
2Vb =Vr1 + Vr2.
Vb = (Vr1 + Vr2) 1/2.

lets find Vr1, which is distance d / time taken during upstream i.e Vr1 = d/4,
Similarly, Vr2 = d/(8 + 4/5),
= 5d/44.

in 60 min it is 1 hr so, in 1 min it is 1/60 hrs and in 48 min it is 1/60 * 48 = 4/5 hrs }
Putting Vr1 and Vr2 values in eq 3, we get -
Vb = 2d/11.

Putting value of Vb in eq 1 we'll get;
Vs = 3d/44.

Therefore, Vb/Vs = 8/3 Ans.

Reshi said: (Jun 7, 2019)  
Thanks @Bindu.

Shifali said: (Jul 25, 2019)  
Let the speed of the boat is u and that of the stream is v.
Time for upstream (u-v) is 528min and time took for downstream (u+v) is 240 min.
Distance covered is the same.

Since, D1=t1*(u-v) and d2= t2*(u+v).
And, d1=d2
So, t1*(u-v) = t2*(u+v).
(U-v)*528 = (u+v)*240
=> u/v = 8/3;
That is 8:3.

Vatshayan said: (Sep 24, 2019)  
An easy way to solve.

Let the speed of boat and water be x km/hr and y km/hr respectively.

Upstream = x-y km/hr.
Downstream = x+y km/hr.

[8+(48/60)](x-y) = 4(x+y)(SINCE DISTANCE IS EQUAL).
8+4/5(x-y) = 4x + 4y.
44/5 x - 44/5 y= 4x + 4y.
44/5x - 4x = 4y + 44/5 y.
24x = 64 y.
x/y = 64/24.
x/y = 16 / 6.
x/y = 8/3 (answer).

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