Aptitude - Problems on Trains - Discussion


A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

[A]. 230 m
[B]. 240 m
[C]. 260 m
[D]. 320 m
[E]. None of these

Answer: Option A


Relative speed = (120 + 80) km/hr

   = 200 x 5 m/sec

   = 500 m/sec.

Let the length of the other train be x metres.

Then, x + 270 = 500
9 9

x + 270 = 500

x = 230.

Meenu said: (Jul 23, 2010)  
In this solution how you are multiplying 5/18 with 200.

I can't understand that wll you please explain me that.

Ajantha said: (Aug 10, 2010)  
Hi meenu,
Total speed(Relative speed) of two trains=120+80=200km/hr
we derived this from km/hr to meter/sec
=200*5/18 (bcas1000/3600=5/18)

Pavan said: (Oct 6, 2010)  
Why you add X and 270 ?

Randhir said: (Nov 17, 2010)  
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:

The time taken by the trains to cross each other =(a+b)/(u+v)

Then time is 9 sec, a=270 metres, b=x metres, u=120 kmph,
v=80 kmph

Therefore 9=(270+x)/(120+80)*5/18
we multiply (120+80) by 5/18 because converting kmph into m/sec

Arulmozhi said: (Dec 24, 2010)  
Hai friends,

Having any other shortcut method to this problem?

Pankaj Kumar Marskole said: (Jan 4, 2011)  
Time taken crossed the train=length of the both train/length of the speed.

Let length of the 2nd train is x.

9= (270+x)/(100/3+200/9).


Yogesh said: (Mar 13, 2011)  
Pleas let me know, where 100/3 comes from ?

Nareen said: (Apr 8, 2011)  
Short cut Method
Relative speed = (120 + 80) km/hr

= 200 x 5/18 m/sec

= 500/9 m/sec.
= 500/9*9
= 500 m
= u+v = 500
= 270+v = 500
= 230m

Pramod said: (Jul 15, 2011)  
Two trains are in opposite travelling in the opposite direction. So how can can add their length? It has to be be subtraction. If they are moving in the same direction then add only.

Kpkpkp said: (Jul 25, 2011)  
When two trains move in opp direction you cant add length. Because length of smallest train is common to both. The actual distance travelled will be length of large train only.

Sushma said: (Aug 23, 2011)  
As given: 120+80=200

Let the length of other train be X
then X+270/9=500/9
cross multiply, u vl get
9X + 2430= 4500
.'. X=2070/9

Kadoliya Jitendra said: (May 29, 2012)  
What is kmph?

Krishna said: (Jun 19, 2012)  
The speed & time of the other so we can directly get the length of the other train.

Amar said: (Feb 15, 2013)  
kmph means kilometer per hour(Km/h).

Amudha said: (Jun 14, 2013)  
To find length of one train why we are calculating relative speed?

Aswin said: (Aug 3, 2013)  
Please let me know, where 100/3 comes from?

Sabira said: (Sep 4, 2013)  
Speed = 120+80 = 200 km/hr.

200* (5/18) = 500/9m/sec.

Total length = 500/9*9.

= 500 m.

500 - 270 = 230 is the other train length.

Kd Kannan said: (Jan 4, 2014)  
To aswin:

100/3 and 120 (5/18).

Two values are equal.

It is another form of 33.3.

Santosh Adithya said: (Jan 8, 2014)  
Why there is (x+270)/9 acc. to formula (270+x)/500/9 = 9 right?

Moni said: (Feb 4, 2014)  
Relative speed should be minus from each train speed because the direction is opposite, isn't it so?

Abhishek Pandey said: (Feb 19, 2014)  
Always opposite will add and same will be subtract.

Janani said: (Mar 30, 2014)  
I want to know one thing usually where we use or apply this relative speed concept ?

Mancy said: (Apr 11, 2014)  

The concept of relative speed is still the basic time, speed and distance formula applied to distance between two moving bodies.

In a simple case of the distance.

Formula, a body traveling with a speed of 50 km/h is reducing the gap between its starting point and the finish point by 50 km every hour.
In the relative speed case of the distance formula two moving bodies, traveling at a relative speed of 50 km/h towards/away from each other, are reducing/increasing the gap between them by 50 km every hour.

Hope this help.

Ronit said: (Apr 25, 2014)  
Easy way.

270 + x
---------------- = 9.

x = 499.5 - 270.

x = 229.5.

Maneesh said: (Jun 25, 2014)  
Can anyone please tell me when to add or subtract the given relative speeds.

Jagadheesh said: (Jun 25, 2014)  
How to find that this problem is need to convert km/hr to m/s or m/s to km/hr. Please explain?

Jayaseelan said: (Jun 27, 2014)  
If the two trains cross opposite directions both are cross each other. So we need calculate crossing speed of the two trains. So we must add two trains speeds respectively. We assumed train A cross train B in a particular amount of speed as same as Train B also cross Train A.

Here two respective speeds are happen then only the process completed in a particular Time. Or we assume Train A is stable that time train B only cross Train A that is Train A speed is zero this is the logic I hope now you can understand.

Kumaresan.P said: (Dec 28, 2014)  
Hi friends please help me,

How to identify relative speed and average speed and normal train problems?

Ajit said: (Feb 23, 2015)  
Use the formula, t = a+b/u+v, (train running opposite direction).

Where t = First train passes other train in time.

a+b = Length of train.

u = Speed of first train and v=speed of second train.

Then, 9 = 270+b/(120+80) km/hr.

<=> 270+b = 200 km/hr*9s = 500 m.

Now, b = 500-270 = 230 m.

Sindhu said: (Mar 14, 2015)  
Why we writing denominator 9 for x+270?

Prasad said: (Apr 1, 2015)  
How this 5/18 came? Can you solve this ?

Manish said: (Apr 18, 2015)  
Why there you take x+270/9?

Silambuiks said: (Apr 23, 2015)  

5/18 means.

1 km = 1000 meter and 1hr = 3600 second.

Convert Kilometer per hour into Meter per second.

Divide the value of 1000/3600 its answer is 5/18.

Karn Sharma said: (May 23, 2015)  
Trains are move in opposite direction. But out of speed n distance one quantity is subtract but in the solution of this question both are added. Please explain I can't understand.

Priya said: (Jun 3, 2015)  
Opposite direction: Adding.
Same Direction: Subtract.

Anurag said: (Sep 6, 2015)  
D = S*T = 270+x = 500/9*9.

So x = 500-270 = 230.

Swathi said: (Mar 2, 2016)  
Thanks alot. It is very helpful to me.

Arun said: (Mar 9, 2016)  
When we add the relative speed when substract please tell me?

Hannan said: (Apr 17, 2016)  
It's simple and just take it easy.

When two trains running on the same site then relative speed is add, running in opposite site then we subtract it.

Krishna said: (Aug 21, 2016)  
Thanks Indiabix, because of this discussion section I can understand that tricks.

Ash said: (Oct 14, 2016)  
Please explain this step 500/9 * 9.

Swanand said: (Dec 27, 2016)  

Can we do like this?

200 * 5/18 = 55.6

In above step is it correct or not, because after all post are look like step following.

200*5/18= 500/9 m/s .

Why not 200 * 5/18 = 55.6.

From above my step will be;
55.6 = (270+x)/6.
(270 + x) = 55.6 * 6 = 333.33.
x = 333.33 - 270 = 63.3 m.

Why not?

Dalton said: (Feb 28, 2017)  
It's simple and just take it easy.

When two trains running on the same site then relative speed is add, running in opposite site then we subtract it.

Nikita said: (Mar 4, 2017)  
Right. But in the question trains are running in opposite side.

So speed is subtracted ie 120-80 = 40.

Am I correct?

Srujana said: (Apr 2, 2017)  
Why we writing denominator 9 for x+270?

Sam said: (May 20, 2017)  
Explain the following step.

x+270/9 = 500/9.

Murugan said: (Jun 8, 2017)  

Use this formula distance/time = speed.

Sathish said: (Aug 11, 2017)  
Another train's speed and time is already given from that we can calculate the trains length easily why we go for oppostie train?

Gaurav said: (Sep 19, 2017)  
Relative speed is 120 +80 =200.
Now l =s*t =200*5/18*9=500,
Now, the total dist minus 500-270=230m.

Umar Bodha said: (Jan 5, 2018)  
Trains running in opp directions.

Relative speed 120+80 =200.
By converting into m/s,
200*5÷18 =500/,
We know by formula
Let x be the length of another train
X=500-270= 230.
So, x=230m.

Sarang said: (May 4, 2018)  
Distance =speed *time,

Nilkant said: (May 5, 2018)  
Please, tell me when to find relative speed?

Reeha said: (May 12, 2018)  
Relative speed is to be found when two moving objects or trains are given.

Bablu said: (Jul 19, 2018)  
What will happen if both trains are in the same direction as we relative velocity we can subtract but how the equation will come?

Please tell me.

Pari said: (Oct 5, 2018)  
If we want to find kmph means 15/8.
mph means 8/15 simple formula.

Ramya said: (Nov 16, 2018)  
On cross multiplication we get,

9 (500) =4500.
Then, 9 (270+x), 9 goes to another side.

Finally, we get 230.

Anomie said: (Aug 14, 2019)  
What we know is:

t1 length=270m.
t1 speed = 120km/h or 33.33m/s.
t2 length = x,
t2 speed = 80km/h or 22.22m/s.
total speed = 9 seconds.

We need to find the relative speed, so its done like this because the trains are moving towards each other.

33.33m/s+22.22m/s = 55.55m/s.

Now we have all the information we need to solve the length of train 2.

-------------- = 9s.

Now we find the total length of both trains combined. We use the information we have. 55.55m/s is now converted to its opposite function, from division to multiplication. 55.55m/s * 9s = 499.95m.

So 499.95m is the total length of both trains combined, so now we can solve train 2's length by completing this final equation.

x= 499.95m-270m = 229.95m. round up to 230m, therefore train 2's length is 230m.

Madhav Kulkarni said: (Feb 2, 2020)  
Train Length=270m.

Time= 9.

Train2 Length= X.
Speed of Train2=80km/h=80*(5/18)=21.6.

Relative Speed=32.4+21.6=54.00.
Relative Length=270 + X.




Then How come 230?

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