Aptitude - Problems on Trains - Discussion

@Agggy.

we add the length of the the train and tunnel because the train is said to have crossed the tunnel if and only if its entire part including the the very last end of it leaves the tunnel.

so if the train has crossed the tunnel in 1min then it would have covered the entire length of the tunnel and a certain distance outside the tunnel (the distance covered by the train until the very last end of the train leaves the tunnel).

So,
that 'certain distance' = length of the train.
.A______x______.B.______800______.C.

where x is the length of the tunnel and the length of the train is 800 m.
the total distance covered by the train is x + 800.

DISTANCE = X+800 m
SPEED = 78 km/hr
TIME = 60sec.

convert speed from km/hr to m/s.
SPEED = 78x1000/60 x 60.
SPEED = 65m/s.

distance /speed = time.
X + 800/65 = 60,
X + 800 = 60x65/3,
X + 800 = 3900/3,
X + 800 = 1300,
X = 1300 - 800,
X = 500.

Length of the tunnel = x
length of the train = 800
relatively (x+800)
-----------------------
train crosses the platform 78 km/hr , we have to convert km/hr to m/s so the formula is 5/18 i.e., 78*(5/18)=65/3.

formula for calculatind the distance is
DISTANCE= SPEED*TIME

TIME is given as 1min i.e., 60 sec
SPEED =65/3

distance = 65/3 * 60
distance = 1300

relative length (x+800) = 1300
x = 1300- 800
therefore x= 500

Hi Thanu,

It's so simple ,Frist we convert km/hr in to m/sec becase train length is given in metres, so multiple speed with 5/18; Then it becomes into 78*5/18=65/3m/sec
Now we can find the length of tunnels say it as "x"metres.
use formula
speed=(length of tunnel+length of train)/60;where 1 minute=60 sec
x+800/60=65/3;After calculation x=500

Distance/Speed = Time.

800 + Length of Tunnel/21.6666667 = 60 Secs.

Length of Tunnel = 60*21.666667-800.

Length of Tunnel = 1300 - 800.

Length of Tunnel = 500.

Note:

Distance = Length of Train (Given) + Length of Tunnel (Asked to Find).

Speed = 78 kmph (Given). We convert that into meters per second. Therefore 78*5/18 = 21.6666667.

Why we are converting into seconds we could have converted into meter/minutes, if the train is going in 75km/hr speed means train is going 78000 meters in 60 minutes from here we can execute how much distance the train covers in 1 minutes, after that by subtracting the train length we can execute the tunnel length.

@All.

Please correct me, if my calculation is wrong.

If we convert 78 km/hr into m/s.
So,
78 * 5/18.
390/18.
21.6 m/s.

Now if we put these value.
x + 800/60=21.6,
x + 800= 60 * 21.6,
x+800= 1296,
x= 1296 - 800.
x= 496.

Anyone please clarify this and explain with the correct answer.

It is simple- as a train covers 78 km in one hour so train covers 78000 meter (78*1000 meter) in 60 minuet, so train cover in one minutes is 78000/60=1300 meter train itself length 800 meter so tunnel length = total distance cover by train-train length, 1300-800 = 500 meter.

I do not understand what is the meaning of crossing a tunnel you understand. I think it should mean the moment train head enters the tunnel till its TAIL comes out one can not consider the train is out of tunnel if its head just come out.

Let the speed of tunnel is x.

Length of train is = 800m

Speed of train is = 78km/hr.
Speed in m/s = 78*5/18

Time of crossing tunnel is 1min.
1 min is 60s.

We are finding the length of tunnel = ?
800+x = 78*5/18*60

x = 500

To understand why we use 5/18 so i clarify that to convert km into m we multiply with 1000 and from hours to second we divided by 60*60.

Hence we get 5/18.
Suppose to change 1 km /hr into metre /sec.
1 * 1000/60 * 60 = 5/18.