Aptitude - Problems on Trains - Discussion

Simple method:

Speed = 45 x 5/18 m/sec = 25/2 m/sec.
Time = 30 sec.

Let the length of bridge be x metres.
Then, 130 + x /30 = 25/2.
2(130 + x) = 30*25.
2(130 + x) = 750.
260+2x = 750.
2x = 750-260.
2x = 490.
x = 490/2.
x = 245.

Train goes in 30 sec : 30*45*(5/18) = 375 m.
Its length = 130 m.

Therefore bridges length = (375-130)m = 245 m.

Simple Answer to solve this problem :

Step 1> Speed of the train with respective to bridge is 45 km/hr in terms of m/s is 45*(5/18)=12.5(v-velocity) .

Step 2> let x be the length of the bridge so v=d/t where d=x+130 answer 12.5=(x+130)/30 (t-time).

245(meters) = x.

The length of the train is=130 m.
Lets assume the length of the bridge = x m.

In 30 sec the train traveled a distance of = (x+130)m.
Therefore the speed of the train = (x+130)/30 m/sec.

The speed of the train = 45 kmph.(Which is already given).
Therefore 45 kmph= (x+130)/30 m/sec.
Convert the 45 kmph into m/sec.

Then,

45* 1000/3600 = (130+x)/30.
45 * 100/ 12 = 130+x.
15 *25 = 130+x.
375 = 130+x.
==> x= 375-130= 245 m.
Therefore the the length of the bridge is 245 m.

Length of the train = 130.
Speed of the train = 45km/hr.
Time = 30sec.

Length of bridge = x+length of train.
x+length of train = Speed of the train *time.

x+130 = 45*5/18*30.
x+130 = 375.
x = 375-130.
x = 245.

Why we are subtracting 130 from 375. While train runs on the bridge not off the bridge?

@Nithin.

Distance = speed x time.
So distance = 45*5/18*30.

Distance = 375 (this is the length of both train+bridge).
So we have to subtract train length (130 m).

Distance = 245.

Train length and bridge length is always add thats why we subtracted 130 from 375?

Speed of the Train = 45 km/hr.
Speed of the train in meters/sec = (45*1000)/(60*60) = (25/2).

Distance covered by train in 30 secs = (25/2)*30 = 375 meters.

Now the train having the length 130 meters had crossed the bridge in 30 secs so the length of the Bridge = 375 - 130 = 245 meters.

@Sai.

Your method is fantastic and very easy to understand. Great job! keep it up man. Thanks!