Aptitude - Problems on Trains - Discussion

25. 

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

[A]. 48 km/hr
[B]. 54 km/hr
[C]. 66 km/hr
[D]. 82 km/hr

Answer: Option D

Explanation:

Let the speed of the second train be x km/hr.

Relative speed = (x + 50) km/hr
= [ (x + 50) x 5 ] m/sec
18
= [ 250 + 5x ] m/sec.
18

Distance covered = (108 + 112) = 220 m.

Therefore 220 = 6
( 250 + 5x (
18

=> 250 + 5x = 660

=> x = 82 km/hr.


Rajgowtham said: (Aug 21, 2010)  
How the final answer comes in km per hour? First we are converting into metre per second so we need to convert it into km per hour.

Sundar said: (Aug 22, 2010)  
Hi Raj,

Please note that

At the first step we are taking the speed of the second train be x KM/HR.

At final step we are finding the value of 'x'.

So, the answer is 'x' km/hr.

Thats why the answer is in km/hr.

Vishal Kumar said: (Sep 7, 2010)  
But Raj, When we calculate the speed of second Train, then we also convert the time in hour. But in the above question time write it as it is, without any conversion of time.

If we want result in Km/hr then we also need to change the time in hour because both the trains takes 6 seconds to cross each other.

Srinivas8126 said: (Sep 9, 2010)  
Hi Sundar.

What you said is right we have taken x in terms on km/hr, considering above explanation while converting relative speed we use (x + 50) km/hr both speeds converted into meters/seconds in next step. So final answer will be in m/s how it will be in km/hr?.

Priyavel said: (Dec 9, 2010)  
Hi.

I can't get it clearly. Please anyone explain it.

Ramesh said: (Dec 14, 2010)  
(220)m
----------------- =6 sec.
((250+5x)/18)m/s
here,m and s are cancelled so x km/hr.

Deepa Singh said: (Jun 7, 2011)  
Please solve this part clearly 220/(5x+250)/18=6

Gargi Banerjee said: (Jun 9, 2011)  
Please give an appropriate answer with perticular reason, this is not clear to me.

Ambika said: (Jun 18, 2011)  
Length of the trains=108+112=220m=(220/1000)=(11/50)km

Let the speed of second train be xkm/hr
therefore,relative speed=(50+x)km/hr(since it is opposite direction the speeds should be added)
time=6sec=(6/3600)=(1/600)hr
then solve using the formula time=(distance/speed)
i.e (11/50)/(50+x)=(1/600)
after solving x will be 82km/hr

Muthulakshmi said: (Aug 27, 2011)  
Hai Mr.Ramesh

You are Correct.Thanks for explaining the problem clearly

Dharamjeet Singh said: (Aug 28, 2011)  
How can the final answer come in Km/hr ??

Harisha said: (Sep 10, 2011)  
Here the ans is in km/hr. so frm starting onwards we sould calculate
the problem without converting into m/s.

Let speed of d second train= xkm/hr

Distance covered=(108+112)=220m=0.22km

Time=6sec= 6/3600hr =1/600hr

So
1/600hr= 0.22km/(50+x)
x=82km/hr

Vijayalakshmi said: (Sep 23, 2011)  
Solution for 220
__________ =6 is
(250+5x/18)

220*18
_______ =6 => 220*18=6(250+5x)
250+5x
=> 220*3=(250+5x)
=>660=250+5x
=> 660-250=5x
=>410=5x
=>x=82

Sanjay Sharma said: (Sep 30, 2011)  
I want to explain clearly for those who have confusio b/w km/h & m/s.
Let take v M/s is the speed of the second train.
Thus formula is
T=220/(v+50*5/18)
after solv. it
we get
v=410/18 in M/s
convert v into km/hr
thus
v=410*18/(18*5)km/hr
then
v=82 km/hr.
I think its very clear now

Ankit said: (Dec 14, 2011)  
Nice explanation Sanjay.

Karthika said: (Feb 5, 2012)  
Hey the final answer is in m/s its not in km/h can some one clarify my doubt.

Darshan Kumar said: (Mar 26, 2012)  
@Karthika , see when we take the series 220/5x+250/18=6 than the 18 will go up side and new series came 220*18/5x+250=6 , so here the formula 18/5 km/h is applicable .
I think ur doubt is clear

Thiyam Surjakumar Singh said: (Apr 9, 2012)  
In the equation all the units meter, second get cancelled so the remaining is x only, whose units is km/hr as we have choosen at beginning of the problem. Hence the result is in km/hr.

@Shok Kumar said: (Apr 29, 2012)  
Here we assumed speed of second train as 'x' km/hr which is in km/hr,okay

then in problem it is converted in to m/sec as 'x*(5%18)' okay and

finally we got answer in terms of 'x' whose units are km/hr as

x=82 km/hr,

which can be in m/sec as

x*(5%18) = 82*(5%18) m/sec

Ranjith said: (Oct 4, 2012)  
Total distance of the 2 trains are 220 (108+112) :first don't change anything. Just change the speed 50 km/hr into m/sec.

If we change speed 50 ino m/sec then it will be 125/9. The equation becomes.

(125/9) +x=220/6.

We get x=410/18 m/sec.

Now convert to km/hr we get x= (410/18) (18/5).

X=82.

Ranjith said: (Oct 4, 2012)  
Total distance of the 2 trains are 220 (108+112) :first don't change anything. Just change the speed 50 km/hr into m/sec.

If we change speed 50 ino m/sec then it will be 125/9. The equation becomes.

(125/9) +x=220/6.

We get x=410/18 m/sec.

Now convert to km/hr we get x= (410/18) (18/5).

X=82.

Arunkumar said: (Feb 5, 2013)  
108+112=220.

220/6 is the relative speed per sec.

(220/6)*(18/5)=132 is the relative speed per hour.

Speed of the 2nd train is 132-50 = 82kmph.

Ram said: (Jul 31, 2013)  
Easiest method is,

220*18 = 6(250+5x).

Multiply by 6(250+5x) you get 1500+30x.

3960 = 1500+30x.

Subtract the value of 3960-1500 = 2460.

Then divide by this form,
2460/30 = 82 kmph

Lakshmi said: (Aug 12, 2013)  
Distance = 108+112 = 220m.

Time = 6s.

Effective speed = x+y (+ because in opp direction).

=> let x = 50 kmph in terms of m/s = 50*(5/18) = 250/18.

eff.sp = 250/18+y (since v need to find y).

So distance = speed*time=>220 = (250/18+y)6.

220 = (250+18y)/18*6.

On simplification,

we get, 410/18.

Converting m/s to kmph, (410/18)*(18/5) = 82kmph.

Roji said: (Oct 2, 2013)  
Hey shyam sharma if I do in your method what you said the problem formula not getting answer yar.

t = 220/ (v+50)*(5/18).

t = 6.

v = 82 got directly.

And hence no need 2 convert again 2 m/sec why?

Roji said: (Oct 2, 2013)  
Why should we convert to m/sec as in above problem (x+50)*5/18.

But in answer the required ans in km/hr again why we are taking 5/18.

Can anyone explain me please?

Ashok said: (Oct 25, 2013)  
220/250+5x/18 = 6.

step 1: 18*220 = 3960.
step 2: 250+5x * 6 = 1500+30x
step 3: 3960 = 1500+30x.
step 4: 3960-1500 = 30x
step 5: 2460 = 30x.
step 6: x=2460/30.
step 7: x=82.

Rajata said: (Mar 21, 2014)  
Total distance = 108+112 = 220 m.

Time = 6s.

Relative speed = distance/time = 220/6 m/s = 110/3 m/s.

= (110/3)x(18/5) km/hr = 132 km/hr.

=> 50 + speed of second train = 132 km/hr.

=> Speed of second train = 132-50 = 82 km/hr.

Mancy said: (Apr 10, 2014)  
Given,

Speed of first train = 50km/hr (after convert it into m/s it becomes 125/9m/s).

Speed of second train = ?

Length of first train = 108m.

Length of second train = 112m.

Now, lets take the speed of second train be x m/s.

So by speed formula i.e.

Speed = distance/time keeping the values in this formula we'll get,

125/9+x = 108+112/6 (here we are adding these value b'coz they are moving in opposite direction).

By taking lcm of 9 on L.H.S it becomes,

(125+9x)/9 = 220/6.

By cross multiplication.

6 (125+9x) =220*9.

750+54x = 1980.

54x = 1980-750.

54x = 1230.

x = 1230/54.

x = 205/9 m/s.

But now we've to convert it into km/hr so.

(205/9*18/5) km/hr.

After cancellation it become.

Answer: 82 km/hr.

Prathap Dha said: (Jul 29, 2014)  
Formula : T=(x+y)/(u+v).

Where,
x,y -- Distance.
u,v -- Speed.

6 = (108+112)/((50*5/8)+V).

6v+250/3 = 220.

Therefore, v = 205/9 m/sec.

v = 205/9*(18/5) = 82km/hr.

Sujai Matta said: (Sep 7, 2014)  
Let me explain in details.

First train length, a = 108m.
Its speed, u = 50 km/hr = 50*5/18 m/sec= 125/9 m/sec.

Second train length,b = 112m.
Let, its speed, v = x m/sec.
Each other crosses in 6 sec.

So, we have, t= ((a+b)/(u+v)).
6= ((108+112)/((125/9)+x)).

(125/9)+x = 220/6.
x = (220/6)-(125/9)= 205/9 m/sec.

Converting in km/hr.

(205/9)*(18/5) = 82 km/hr.

Student said: (Nov 16, 2014)  
Well I have a doubt, how did you get 5/18? Sorry if it is a stupid question!

Rocky said: (Nov 18, 2014)  
I would like to bring this error to your notice that it is 82 m/s and not 82 km/hr.

Sathish said: (Nov 21, 2014)  
Hai I have another option.

D = 220.
S = 50 kmph.
T = 6.
Other speed = x.

So speed = (x+50)*5/18.

T = D/S. Find T subtract 50 that's answer = 82 kmph.

Sathyapriya said: (Nov 29, 2014)  
Let me explain in detail.

Let the speed of second train be xkm/hr.

Therefore, relative speed = (50+x)km/hr (since it is opposite direction the speeds should be added). Then no need to confuse yourself by converting the speed to m/s.

Take it as it is, so as to get our answer in km/hr (as the given options are in km/hr). Now just convert the distances 108m & 112m into km/hr.

So add the distances & then convert it.

D = 108+112 = 220m = (220 x 18/5) = 792km/hr.

So now distance is in km/hr.

T = D/S.
6 = 792/(x+50).
6x+300 = 792.

Therefore x = 82km/hr.

Shree said: (Jan 16, 2015)  
(108+112)/6 = 50 + x.
(220/6)*(18/5) = 50 + x.

132 = 50 + x.
x = 82 Km/hr.

Prathiba said: (Jun 12, 2015)  
How does 660 comes in last step?

Rishav Kumar said: (Sep 8, 2015)  
Yes answer is correct but checking through reverse process.

Let x = 82 km/h and we have find time to cross each other. Then then the answer will come 6 sec. So it is correct.

Arun said: (Oct 7, 2015)  
Relative speed = x+50 km/hr.

6 = 220/(x+50)*(5/18).

5/3 = 220/(x+50).

x+50 = 132.

x = 82 m/sec.

Please explain, how km/hr.

And one more method.

6/3600= (220*10^-3)/(x+50).

x+50 = 600*0.22.

x = 142-50.

x = 92 km/hr.

Now I am totally confused. Please help.

Sajan said: (Nov 28, 2015)  
Distance = (220/1000) km {Want to convert meter into kilometer).

Time = (6/3600) seconds {Second into hours - one hour has 3600 seconds}.

Distance/Time = Speed.

= (220/1000)/(6/3600) = x+50 km {Opposite speed should be added).

Now without converting, follow normally:

220/6*3600 = (50+x) speed (If goes 220 m within 6 seconds, what is the distance per hour or 3600 seconds).

132000 m per hour = (50+x).

So, 132 kilometer = (50+x).

x = 132-50 = 82.

Rutika said: (Jan 4, 2016)  
S = D/T.

So, D = 108+112 = 220 m.

= 220/1000 km/hr.

T = 6 sec = 6/3600 = 1/600 hr.

S = 50 km/hr.

We assume second train speed 'x'.

Relative speed = 50 km/hr+x km/hr.

S = D/T.

= 50+x = 220/1000*600.

= 50+x = 22*6 = 50+x = 132.

x = 82 km/hr.

Moin said: (Mar 1, 2016)  
But can't do in direct formula of a + b/u + v = t? Then finding us there.

Rabvah said: (Apr 24, 2016)  
50*5/18 = 13.889 m/sec.
108 + 112/13.889 + x = 22.778.

Since it has to be in km/hr.
23.778*18/5 = 82 km/hr.

Priyanka said: (Jun 22, 2016)  
Total distance = 112 + 120 = 220 m.

Time = 6 sec.

Relative speed = total distance / time,

=> 220/6 m/s

Speed in km/h,

=> 220/6 * 18/5 = 132.

Speed of second train = relative speed - speed of 1st train,

=> 132- 50 = 82 km/h.

Azam Khan said: (Jul 27, 2016)  
How Comes 5 in answer? I can't Understand please explain this.

Ravi said: (Aug 9, 2016)  
Simple solution method:.

Length of train 1st is = 108m.

Speed of train 1st is = 50km/h => 50 * 5/18 == 125/9 m/sec.

Length of trian - 2nd is = 112m.

Now, let the speed of 2nd tarin is = x m/sec.

Relative speed =x + (125/9).

Relative distance = 108 + 112 = 220 m.

Time = 6 sec.

Now, s = d/t.

=> x + 125/9 = 220/6 (therefore 220/6= 110/3).
=> x = (110/3) - (125/9).
=> x = 205/9 m/sec (205/9) * (18/5).

x = 82 km/h answer.

Apoorv said: (Oct 3, 2016)  
Sir, if the train is moving in an opposite direction the total distance one has to cover is the larger length. So why have we added the two?

Amitesh said: (Oct 26, 2016)  
The solution is not clear for it. Can anybody solve it easily?

Amitesh said: (Oct 26, 2016)  
220/6 = 250 + 5x/18,
By solving it we get,
3960 = 1500 + 30x,
2460 = 3x,
So, x = 82.

Soumitra Das said: (Dec 5, 2016)  
D = 108 + 112 = 120
Converting the speed of 1st Train = 50x 5/18 m/s
Let the speed of 2nd Train= V m/s

We get,

220/ (50x 5/18) + V = 6 sec

=> 220= 6x(250+18V)/18,
=> 220=(250+18V)/3,
=>660= 250+18V,
=>18V=390,
=> V= 390/18 m/s.

Converting the speed of the second Train we Get
=> (390/18) x (18/5)
=> 78 Kmph.

This is the right answer

Soumitra Das said: (Dec 7, 2016)  
Sorry I make a mistake in my last comment.

D = 108 + 112 = 120.
Converting the speed of 1st Train = 50x 5/18 m/s.
Let the speed of 2nd Train= V m/s.

We get,

220/ (50x 5/18) + V = 6 sec.

=> 220= 6x(250+18V)/18,
=> 220=(250+18V)/3,
=>660= 250+18V,
=>18V=410,
=> V= 410/18 m/s.

Converting the speed of the second Train we Get,
=> (410/18) x (18/5).
=> 82 Kmph.

This is the right answer

Ashwin Kumar said: (Dec 11, 2016)  
@Ashok.

How you get 220/250 + 5x/18?

Sriram said: (Aug 17, 2017)  
We have got v (kmph) if it had been v * 5/18 then we would have gotten speed in m/s.

Gangani said: (Jul 4, 2018)  
First take 220/6=36.66 m/s.

Now convert into km/h so 132km/h.
and minus 50km/h from 132 - 50 = 82km/h.
Thanks.

Nileshshelar said: (Oct 19, 2018)  
(Total distance covered) ÷ (net speed) = time.
Mtrs/(mtr/sec) = sec.
220/(50+x) * 5/18=6,
So x=82.

But the unit is now mtr/sec because all we have converted into mtrs and seconds.

Gopal Sunar said: (Jan 17, 2019)  
Thank you @Soumitra Das.

Nagesh said: (May 23, 2019)  
Thank you @Das.

Arkadev said: (Jun 27, 2019)  
Relative speed =220/6 * 18/5=132.
Second trains speed =132-50 = 80.

Prity Sahay said: (Aug 17, 2019)  
If everything is converted into m/s then the answer will also be 82m/s not 82 km/hr.

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