Aptitude - Problems on Trains - Discussion

Consider u r standing on a platform.
When someone asked you how far is the train from the platform ur answer value reduces as the train is the train is closer and closer.

When it is moving away which means in opposite direction the distance increases.

So when the same thing assumed between two trains when they are moving in opposite direction from you the distances of both trains increases and total distance of two trains from you will be t1+ t2.

Than same can be applied to the speed or time.

5/18 is calculated value for 1000 kms / 3600 seconds (km/hr) used to convert km/hr in meter per second and the reverse 18/5 for meter per second into km per hour.

Hi, @Karthik.

The relative speed between two trains is =90 Km/hr--> equation1.
But 1 Km=1000 m; and 1 hr=3600 sec.

Now these two values are substituted in equation1 because we want to convert Km/hr into m/sec because the answer was in m/sec. =(90*1000)/3600 or 90*(1000/36000).

Simplify above like in thousand two zeros are cancelled by denominator value of two zeros(3600), then we get 90*(10/36).

Then again simplify the equation by using 2 table cancel the 10 and 36, then we get 90*(5/18), then it is again simplified using 6 table cancel the 18 and 90, then we get 25*(5/3).
so, this is again simplified, and got 125/3.

Don't worry about it.

Use simple idea of relative speed and distance.

S = U*T.

Where S = Relative distance.
U = Relative Speed of train.
T = Time taken by train.

Note:

1. If one train is crossing bridge/platform then take relative distance as "sum of length of train and bridge/platform".
2. If both are in same direction then subtracts the speeds.
3. If both are in opposite direction then add the speeds.
4. If one Train is crossing "man" then his speed is "Zero".

@Vijju.

You are right that we have to consider the faster train's length. But you have to keep concern about that both trains starts from opposite direction. So, both trains cross each others at the same time. So, when they cross each others from the opposite direction; so in that case individual length is not important. But total length of the trains is important to measure the total distance/way what they cross each others.

Now im telling how the answer came 48 sec and doubt about 125/3.
See, the relative speed of the train in the opposite direction will be always A + B.
THEN, 90 + 60 = 150 KM/HR.

Then convert into m/s 150 * 5/18 = 125/3 clear,
Now total distance = 2 km = 2000mtr,
Required time = (2000/125/3.
= 2000/1*3/125 = 48 answer in above question this step is by passed because this is common thing which is everyone knows.

@Mohd. Nafees
why you multiply 2000 with 3/125. why it is not multiply by 125/3????

apply this formula in this step:
length of the train= speed*time taken
here speed of the train is (125/3)in m/sec and length of the train is 2000m.
time is required so assumed as x ;
now apply above formula :
2000=(125/3)*time
2000*3=125*time
6000=125*time
finally we get time=(6000/125)=48sec.

have a nice day!

Soluution,
First, the direction of the train is opposite so we will add the speed s1+s2..
Then, the length of the train first and second train t1+t2..
S1 + S2=60 + 90 = 150 km/hr.
T1+T2 = 1.10 + 0.9 = 2 km.

Formula,
t= d/s
t = 2km/150km/hr
1km-1000m
So, 2km - 2000m.

t = 2000m/150 *5/18 m/sec.
Convert km/hr into m/sec;
(150 km/hr -> 5/18 m/sec).
After solving we will get,
t= 48sec.

Can anyone explain why we are taking 2km as the distance ?

"The time taken by the slower train to cross the faster train" means the time taken by the tip of the slower train's engine to travel from faster train's engine to faster train's end ... right ??

So ideally the distance should be .9km (length of faster train). However the speed will remain 150 kmph.

@Jyoti:

When slower train will cross the faster train, it means both train has crossed each other , so don't get confused with that.

The question is simply asking when both train will cross each other.For that total distance will be the sum of the lengths of both trains. And total(relative) speed also will be the sum of speeds of both the trains.

@Sekhar.

If Initially you are not convert distance and speed in meter and m/s then after getting time you multiply only by 3600 for getting 48 sec.

Because Unit of Time is Only hour or seconds.
As T=D/S
So unit of T=(Unit of distance)/(Unit of Speed)
So you get Unit of Time is Only hour or seconds

Time T=D/S = 2/150=1/75*3600=48 sec.