Aptitude - Problems on Trains - Discussion

We can do this problem in another way.


Length of train travelling at 48 km/h = 'X' metres;
Let speed of the train travelling at 48 km/h be 'u'.

Length of train travelling at 42 km/h = 'X/2' meters;
Let speed of the train travelling at 42 km/h be 'v'.

Time taken by both trains to cross each other = (X+X/2)/(u+v) {FROM FORMULA 8 IN IMPORTANT FORMULAS}.

u=48 km/h = 13.33 m/sec {CONVERTED TO metres/sec}
v=42 km/h = 11.66 m/sec {CONVERTED TO metres/sec}.

i.e, (X+X/2)/(13.33+11.66) = 12 sec.
i.e on solving , (3X)/(49.98) =12 sec.
X=199.2 metres.
Let platform length = 'Y' metres.

Time taken by a train of length 199.2 m to cross-platform of length Y m = time taken by train to cover (199.2+Y) metres. {FROM FORMULA 5 IN IMPORTANT FORMULAS}.

i.e, 45 sec = (199.2+Y)/(48 km/h).
i.e, 45 sec =(199.2+Y)/(13.33 m/sec).

From this Y=400.65 metres ; approx = 400 metres.

According to the problem,

First let us take length of the first train as "x"

So the length of the second train is half of the second train so it is half of x
So the total length is "(3/2)x"

and given that the two trains are travelling in opposite directions so that their relative speed = (48+42)km/hr.
now convert into m/s so it is 90*(5/18) =25 m/s.

from basic rule s = d /t;

25 m/s = ((3/2)x)/ 12 sec
by solving it we get x = 200m

and given that time required to pass platform is 45 sec

and length of platform = z
48 * (5/18) = (200+z) m/ 45 sec

by solving it we get finally 400 m

Let length of first train be 'L' therefore length of 2nd train is 'L/2'.

Now, since trains are moving in opposite direction, there relative speed is,

(48+42) km/h = (L+L/2) /12.

(48+42) x 5/18 m/sec = (3/2 L) /12.

90 x 5/18 x 12 = 3/2 L.

300 = 3/2 L => L = 300 x 2/3 => L = 200 mtrs.

Now with respect to Plateform, Let distance of Platform be 'X'.

Therefore, Total Length = 200 + X and Speed is of first train i.e. 48 Kms/hr & time = 45 secs.

48 kms/hr = 48x5/18 mtrs /sec.

Therefore, 48 x 5/8 = 200 + X/45.

(48x5x45) /18 = 200 + X => 600 = 200 + X => X = 600-200.

X = 400 mtrs.

@Sai.

RS=(48+42)=90kmh
Then 90*5/18=25m/s.

So, First Train + 2nd Train Total Length = 25m/s * 12second = 300M.

ATQ,
First Train = 200M.
2Nd Train = 100M.

Now,
First Train Speed in Ms = 48 * 5/18 = 40/3.

So, First train+platform Total Length = 40/3 * 45 = 600M.
So, platform length is =600M-200M = 400M.

@Reka.

We use first train Speed because it's moving towards the platform and more important For ATQ we use First train speed we can't use both the speed because 2nd train is moving opposite.

Speed of two trains in opposite direction = (48+42) = 90 km/h.

Converting it to second (90*5/18)= 25m/s.

Train passed another train = total length of the two train = 25m/s*12s= 300m As another train is half of the another train = the train length is 2*300/3 = 200m.

After the train it crossed one railway platform so we have to come to the first speed 48*5/18 = 40/3.

Then crossing time = 40/3*45 = 600 it included with the train length.

So platform length is 600-200 = 400m.

Answer will be be 400 meter because you guys did not read question properly.

It is clearly mention mean n last line the word "it" is referred for first train.

So now you have length of first train, its time to cover platform of length y meter and its speed 45 km/hr now use simple formula.

s(48km/hr) = (length of train(200)+length of platform(y)) /time to cover/cross platform(45 sec).

So y=400 meter.

The total distance that the trains have to travel to cross each other is "x" and not " x + x/2 ". Where "x" is the length of the longer train. This is where we are going wrong.

Then the length of the longer train would come out to be 300m and the length of the platform will come out to be 300m too.

Which adds up to 600m. And the train will take 45s exactly to cross the platform and the answer.

Opposite direction,so speed of 2 train= 48+42=90, so length of 2 trains is =90*12*5/18=300. Given that 2nd train is half of the first train, so the length of first train= 200 m.

Now, length of platform =(200+x)18/48 * 5 = 45.
Solving, x = 400 m.

@Riya.

In the question it is mentioned that first train completely passes the second train and also passe the platform that's why we have to consider the first trains speed.

For that first we have to calculate the first train.

The answer isn't correct. It should be 600m.

Proof: If you go by other way taking length of the platform as 400m and time as 45 seconds.

Then the speed of the train would come as: (400/45)*(18/5)=32kmph(which isn't true)