Tip #1: Understand the concepts involved in a train crossing a pole or a platform

1. Time taken by a train of length L to pass a pole or standing man or a signal post is equal to the time taken by the train to cover distance L.

2. Time taken by a train of length L to pass a station of length b is the time taken by the train to cover the distance (L + b).

Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Solution:

Time taken to cross a pole = time taken to cover distance equal to its own length.

Speed of the train in m/s = 60 x 5 / 18 = (50/3) m/s.

Length of the train = Speed of the train x Time taken to cross the pole

= 50/3 x 9

= Length of the train = 150m.

Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:

Speed of the train in m/s = 54 x 5 / 18 = 15m/s.

Length of the train = 15 x 20 = 300m.

Distance traveled in 36s = 15 x 36 = 540m. (This is the length of the train + platform combined)

Tip #2: For problems on 2 trains, use the concept of relative velocity

1. If two trains of length a and b are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = (a + b) / (u + v).

2. If two trains of length a and b are moving in the same direction at u m/s and v m/s, then time taken by the faster train to cross the slower train = (a + b) / (u - v) .

Question: 2 trains of length 137 m and 163 m are running towards each other and speeds 42 km/hr and 48 km/hr respectively. In what time will the two trains cross each other?

Solution:

Relative velocity = 42 + 48 = 90 km/hr = (90 x 5/18) m/s = 25 m/s. (Opposite directions)

Time taken to cross each other = 300 / 25 = 12 sec.

Question: 2 trains running in opposite directions cross a man standing on the platform in 27s and 17s respectively and they cross each other in 23s. Find the ratio of their speeds.

Solution:

Let the speeds be x m/s and y m/s respectively.

Then, length of 1^{st} train = 27x and that of 2^{nd} train = 17y.

Time taken to cross each other = (27x + 17y) / (x + y) = 23.

= 27x + 17y = 23x + 23y.

= 4x = 6y.

= x: y = 3 : 2.

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Trains

Problems on Trains: Problems on Trains Formulas and Shortcuts, Train Problems in Aptitude Questions with Solutions