Problems on Trains

[Q] If a train running at a speed of 72 km/hr crosses a post in 20 seconds. What is the length of the train?
(a) 200 m
(b) 300 m
(c) 400 m
(d) 500 m

Solution

Answer   (c)
Explanation
----
 Speed of the train, s = 72 km/hr = 72000/3600 m/s = 720/36 m/s

Time taken to cross the post, t = 20 seconds.

Distance Covered, (distance = speed × time) = st = (720/36)× 20 = 400 m .

[Q] A train runs at the speed of 90 kmph and crosses a 500 m long platform in 30 seconds. Find the length of the train?
(a) 150
(b) 250
(c) 350
(d) 450

Solution

Answer   (b)
Explanation
----
Speed of train = 90 kmph = 90 × (5 / 18) = 25 m/s

Distance covered = (500+ L), where L = length of the train.

Time taken to cross the post = 
[(Combined length of train + platform) / speed of train] = 30seconds

=> (500 + L) / 25 = 30

=> 500+ L = 750

=> L = 250m

[Q] A train having a length of 500 m passes a post in 50 seconds. Find the time taken by it to pass a platform having a length of 500 m?
(a) 200 seconds
(b) 100 seconds
(c) 300 seconds
(d) 400 seconds

Solution

Answer   (b)
Explanation
----
speed of the train (s) = (distance / time) 

= 500 / 50 = 10 m/s

Time taken to pass the post =
 [ (combined length of train + platform) / time ] =

= (500 + 500) / 10 = 100 seconds

[Q] A train 400 m long runs with a speed of 54 km/hr. What time will it take to pass a platform of 200 m long?
(a) 40 seconds
(b) 20 seconds
(c) 30 seconds
(d) 50 seconds

Solution

Answer   (a)
Explanation
----
Speed = 54 km/hr = 54 × (5 / 18) m/s = 15 m/s

Time taken to pass the platform =
 [(Combined length of the train + platform) / speed of train ]

= 400 + 200 = 600 meter

Time taken to cross the platform = 600 / 15 = 40 seconds 

[Q] Two trains, each of length 150 m are moving in opposite directions. They cross each other in  10 seconds. If one is moving twice as fast the other, then find the speed of the faster train.
(a) 20m/s
(b) 40m/s
(c) 10m/s
(d) 60m/s

Solution

Answer   (a)
Explanation
----
Total distance covered = (combined length of both trains) =
150 + 150 = 300 m

Time taken to cross each other = 10 seconds.

let the speed of slower train = s .

Then the speed of the faster train = 2s

So,Relative speed = s + 2s = 3s (both train moving in same direction)

3s = 300/10 m/s = 10 m/s

=> s = 10 m/s

=> Speed of the slower train = s = 10 m/s

and, Speed of the faster train = 2s = 2 × 10 m/s = 20m/s