Aptitude - Problems on Trains - Discussion


Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

[A]. 30 km/hr
[B]. 45 km/hr
[C]. 60 km/hr
[D]. 75 km/hr

Answer: Option C


Let the speed of the slower train be x m/sec.

Then, speed of the faster train = 2x m/sec.

Relative speed = (x + 2x) m/sec = 3x m/sec.

(100 + 100) = 3x

24x = 200

x = 25 .

So, speed of the faster train = 50 m/sec

   = 50 x 18 km/hr
3 5

   = 60 km/hr.

Ravi said: (Aug 13, 2010)  
What is (100+100)/8=3x?

Jagdish said: (Aug 19, 2010)  
I don't understand how is speed of the faster train = 50/3 m/sec.

Nagashree said: (Aug 26, 2010)  
In the question they have mentioned that we have to find the train which is twice as fast the other hence we have to multipy (25 x 2)/3 = 50/3.

Manoj said: (Oct 6, 2010)  
Please guide me step by step in calculation.

Jyoti said: (Dec 7, 2010)  
Dear ravi this is speed of first train +speed of second train=relative speed of both trains moving opposite.

Jelli said: (Dec 11, 2010)  
It's very simple i think

WKT t=(a+b)/(u-v)

t=8s,a=b=100m,u=x,v=2x(twice fast of other)
then in the problem they asked length of the faster train is 2x=60m.

Arun said: (Dec 26, 2010)  
What is 5/18? How the value will come?

Nayana said: (Dec 28, 2010)  
Hi Arun,
Here we are converting km/h to m/s
so 1km=1000 meters
1hr=3600 sec
1km/h=1000/3600 m/s
1000/3600=5/18 m/s

Mini said: (Dec 29, 2010)  
Hi @jelli, I think this is correct.

length of each train=100 m
let speed of one train=x km/h
other is moving twice as fast the other i.e=2*x km/h
they are asking the speed of faster train which is 2*x
here we land up with x=30

So 2*30=60m

Ikram said: (Jan 5, 2011)  
Hey Jelli...

1) if 2 things moves in same direction:
time they meet t=(x+y)/(u-v)
where x,y-distance of trains or smthng
u,v-speed's in mps.

2) if 2 things moves in opposite direction:
time they meet t=(x+y)/(u+v)

Seema said: (Jan 17, 2011)  
If these two trains are moving in opposite direction then how can we add their distance.

Kumaran6248 said: (Jan 19, 2011)  
Here I wanna know! how we suppose to have 2x as fast train. Can any one suggest me"""If one is moving twice as fast the other""". And what about this?

Vel said: (Jan 31, 2011)  
Hi seema rules wise we have to add the distance, relative speed based on the direction of both trains (same:-, opposite:+).

Akber said: (Mar 25, 2011)  
Assume one train is moving with X speed than other is twice faster it means 2x

look normal speed =x
twice the above speed=2*x=2x

Kavitha said: (Apr 11, 2011)  
I didn't understood how can I clear this problem?

Lavanya said: (Oct 8, 2011)  
I don't understand please explain it brief.

Adityabala said: (Oct 13, 2011)  
Now study the problem carefully the given data is
two trains moving in opposite direction . that means we add them 100+100=200mts

to cross these 200mts it takes 8 secs ok
now, they have asked to find the speed of the faster train if the speed is twice the slower train , this is given in the question.

Now ,


speed=200mts/8secs ok
as options are given in km/hr , we have to convert speed to km/hr

So we multiply with 18/5
well (200mts/8secs)*18/5=(200/8)*(18/5)=90km/hr
these is the total speed .

Now they asked us to find the speed of the train twice the other train

Let the speed of first train =xkm/hr

Speed of other train should be twice=2x km/hr

So we have got total speed as 90km/hr
speed of one train is 30km/hr.

So they asked twice the speed of train

So we get 2x=2*30
Now if we add 30+60=90km/hr

We got the total speed

The speed of the faster train is 60 km/hr

Dinesh said: (Dec 2, 2011)  
In this problem how we can take 50/3?

Abhinav said: (Jan 22, 2012)  
When the train is Opposite direction, than the relative speed is add to both (100+100)= 200

Shiv said: (Feb 3, 2012)  
Give me short cut.

Sravan said: (Mar 11, 2012)  
if speed of the slower train be x m/sec.

Then, speed of the faster train y = 2x m/sec=> x=y/2

Relative speed =(x+y)= (y/2+ y) m/sec = 3y/2 m/sec.

(100 + 100)/8 = 3y/2
y=50/3 m/s

speed of the faster train = 60 kmph

Rahaman said: (Mar 20, 2012)  


Vaasudevarao said: (May 4, 2012)  
Speed= d/t (100+100)=200*18/5=90km/h two train speed x+2x =3x 3x=90; x=90/3 x=30 so faster train speed is 2x =60

Harpreet Singh said: (Jan 23, 2013)  
Why multiply 50/3*18/5 in the last?

Thenmolzhi said: (Mar 28, 2013)  
Relative speed = (x+y);
x = x;

y = Twice faster than 'x', So 2x;
y = 2x;

Relative speed = (x+2x) = 3x.

Divya said: (Jun 15, 2013)  
Here there is no need of finding relative speed right? then why we find relative speed?

Charmi said: (Sep 21, 2013)  
How did you reversed the 18/5 and multiplied with 50/3?

Vaibhav said: (Oct 2, 2013)  
Here there is no need of finding relative speed right? then why we find relative speed?

Rajaprabu said: (Nov 16, 2013)  
What is 18/5 and 5/18 ? why we are using please explain?

Swetha said: (Nov 28, 2013)  
Hi @Raja,

5/18 is to convert KM to Meters.

18/5 is to convert Meters to KM.

As, in question it is given in Meters but answer is in meters so have to convert Meters to KM. So we are using.

Mounika said: (Feb 22, 2014)  
What 50/3 I didn't understand this step?

Mancy said: (Apr 9, 2014)  

We supposed the speed of the first train = x.

Nd speed of the faster train which is moving twice as fast the other = 2x (as we have given).

Now, given length of each train = 100m,

Time = 8sec,

Substitute these value in formula.

Time = (distance/speed).

8sec = (100+100/x+2x).

"Here we are adding the values b'coz the trains are in opposite direction with each other, which you can easily understand by reading the formula column. ".

8 = 200m/3x.

By cross multiplication.

24x sec = 200m.

x = 200/24.

x = 25/3 m/sec.

When we convert it into km/hr it becomes.

x = 30km/hr but.

Acc. To question they are asking for faster train which is 2x.

So by putting the value of x in 2x we'll get the correct answer.


Answer = 60 km/hr.

Studybeforexam said: (Oct 16, 2014)  
25/3 + 25/3 = 50/3 i.e. 3 being a common denominator.

Sudha said: (Nov 19, 2014)  
I did not understand how you got 50/3? Please I need a clear explanation.

Sudha said: (Nov 19, 2014)  
When you divide 200/24, you won't get 25/3? So I request you to explain me properly.

Priyesh Jain said: (Jan 19, 2015)  
"D = ST".

Total distance = 100+100 = 200 m.

Relative speed = s+2s = 3s.

T= 8 sec.

Putting these values.

200 = 3s*8.

S = 200/8*3.

S = 25/3 m/s.

Now be need to calculate speed in terms of km/h.

25/3*18/5 = 30 km/h.

Speed of slower train now speed of faster train is 60 km/h that is just double.

Anshul Saraf said: (May 12, 2015)  
Here both trains will not travel the same distance of 100 m. However the sum of distance travelled by both trains will be 200.

Shiva said: (Jun 28, 2015)  
Why you are all talking always 5/18 to convert kmph into m/sec, I can't understand that logic, please explain reason behind that. Thanks in advance.

Khumalo said: (Jul 24, 2015)  
Where is 3 coming from?

Srinu said: (Nov 19, 2015)  
What is formula distance?

Praveen Sharma said: (Jan 26, 2016)  
Here (100+100)/8 = 3x.

200/8 = 3x.

25 = 3x.

So x = 25/3 m/s it is speed of slow train.

We want speed of fast train, it is 2x where x = 25/2 m/s.

So speed of fast train = 2*25/3 m/s.

So 50/3 m/s.

And we convert in km/s using 18/5.

So (50*18)/(3*5) = 900/15 = 60 km/h.

Praveen Sharma said: (Jan 26, 2016)  
How come 3?

Answer - If speed of slow train is x km/h.

In question the speed of fast train is twice to slow train.

So speed of fast train = 2*(Speed of slow train).

So speed of fast train = 2*(x) = 2x.

If trains are moving in opposite direction then we ADD the Speed. And trains are in same direction then we sub speed.

Here train in same direction so we add the speed of both train.

So x + 2x = 3x.

Sam said: (May 13, 2016)  

Super explanation, Thank you.

Vijay Arun said: (Jul 15, 2016)  

Nice explanation.

Jai said: (Jul 16, 2016)  
If 1st train accelerated by 0.3 and 2nd 0.2 then how to solve it?

Qweg said: (Aug 18, 2016)  
In this, we are not considering the distance that is between them? Should it be considered too?

Navin said: (Jan 28, 2017)  
x = 25/3

So, speed of the faster train = 50/3 m/sec.

I can't understand these steps please help me.

Sonam said: (Mar 24, 2017)  

Nice explanation. Thanks.

R.Rakesh Kumar said: (May 28, 2017)  

In question they have mentioned to calculate the speed of faster train i.e to calculate 2X
X=25/3 is the speed of the slower train and ( " If one is moving twice as fast the other" given in question).

2 * X = 2 * 25/3 => 50/3.

K.Ratnababu said: (Jun 24, 2017)  
This is another way.
two trains opposite direction 100m+100m=200m.
200m to cover 8 seconds then,
(200m 8sec
? 3600sec
90000m that means 90k).
3600sec that mean 1 hour to cover 90000m that is 90k/h.
the train speed is 2:1.
total 3 parts.
3parts 90kilometers then,
2parts ?

Garvit said: (Aug 9, 2017)  
Why wasn't the speed of one train 1 considered x and other considered y? Why we're both taken as x?

Sarang said: (May 4, 2018)  
Distance =speed *time,
200=speed *8,
Speed =25m/s,
Converting m/s into km/h.
As we want twice speed so first find single speed.
1+2 one is the speed of first train and 2 twice a second so combing we get 3 now,
Speed =90/3=30.
Now twice speed is 60km/h.

Eudis said: (May 10, 2018)  
From where did 18/5 come? Please explain me.

Reeha said: (May 12, 2018)  

It's the basic conversion principle, From km/hr to m/s we can use 5/18 and the reciprocal for vice versa.

Ganesh said: (May 15, 2018)  
Consider one train x speed and another one is x one twice speed to the other train then x+2x-3x.

Nutan said: (Jun 17, 2018)  
(50/3) * (18/3) = 60 how?

Sunil Bhanovath said: (Dec 3, 2018)  

Why 50/3 taken as speed of the train is 2x so that's why we should take.

Sowdi said: (Feb 18, 2019)  
Thanks for your explanation @Sarang.

Punam said: (Mar 9, 2019)  
How come 50/3?

Manivel said: (Jun 1, 2019)  

Substitute the X value in faster train 2X, 2* (25/3) =50/3. M.

Arifur Rahman said: (Jul 20, 2019)  

The speed of slower train be x m/sec.
The speed of faster train be 2x m/s.

(x+2x)รท2(two trains) = 100/8.

The Speed of faster train = 2x = 2 * 25/3 = 50/3 m/sec * 18/5 = 60km/hr.

Dewansh said: (Oct 16, 2019)  
Why the relative speed is the sum of individual speeds rather than the difference?

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