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# Problems on Ages

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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 remember.here 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.

### 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. Answer: 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.

### 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. Answer: 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. Answer: 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.

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