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Quantitative Aptitude > Important Problems > Problems on Trains
Important Problems

Problems on Trains

Some of the important section in a competition is time and distance. And similar to this part is the problems on the train. Many of the train problems also follow the same procedure. The only difference between the two is the length of the train. Because the train is the moving object and thus we need to consider the length of the moving object instead of a still object. In this article, we will see some train problem.

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Important points to remember on Train Problem 

  • While solving the problems on trains there are some points that you need to are those points:
  • While converting km/hr into m/s you need to use 5/18 x a. Here, ‘a’ is the required answer.
  • The time taken by a train to pass a pole of length ‘l’ meters or a standing man or anything stationary is same as the time taken by the train to cover that ‘l’ distance.
  • When two trains or any objects are moving in the same direction at ‘x’ m/s and ‘y’ m/s, wherein x > y, then their relative speed should be (x – y) m/s.
  • When the two trains are passing in a different direction than their actual speed should be added to the relative speed.
  • If the train is going through a platform, the length it travels should be equal to the sum of both the platforms and the length of the trains.
  • When the trains are moving in a similar direction the difference of their speed is the relative speed of these trains.

Problems on Trains

train problem

Trains going in a different direction.

Q. There are two trains of 89 m and 111 m in length running in different directions. One of this train is running at a rate of 30 km/hr and the other is 42 km/hr. Find the time these trains will clear each other.

Here it is given that the two trains are going in a different direction. So, their relative speeds will be added. Thus, the total speed is 42 + 30 = 72 km/hr or 20 m/s in metres. So, the total time required here is, the total length of the trains/relative speed = 89 +111/20 = 10 seconds.

Solve Problems related to Race here 

Train crossing a platform

Q. A 120 m train is running at a rate of 54 km/hr. This train takes 102 seconds to cross the platform. Find the time it takes to cross the platform.

Here, while crossing a platform, the train will have to travel its own length in addition to the length of the bridge. First, we will convert km/hr into m/s. So, 54 km/hr = 54 x 5/18 = 15 m/s. So, the time required is 222/15 = 14.8 seconds. This is our required answer.

Trains going through a standing pole

Q. Suppose a train which is 220 meters in length is going at 60 km/hr rate. Find the time it will take to pass a man who is walking in the opposite direction at 6 km/hr.

In this question, the length of the man will be considered as 0. So, it will be solved in the same way as above. Thus, the speed of both will be added. Thus, the relative speed is 60 + 6 = 66 km/hr = 55/3 m/s.

So, the required time by the train will be, 220/55 x 3 = 12 seconds.

Practice Questions on Problems on Trains

Q. There are two trains that are running in the opposite direction. Each train has a length of 120 meters. They cross each other in 12 seconds, find the speed of the train.

A. 42 km/hr               B. 48 km/hr                C. 36 km/hr                      D. 54 km/hr

Answer: C. 36 km/hr

Q. There is a which a train running at 60 km/hr crosses in 9 seconds. What is the length of this running train?

A. 130 meters           B. 140 meters              C. 150 meters                   D. 160 meters

Answer: 150 meters

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