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**Problems on Train**

### Problems on train are now common in competitive exams and they are all about finding the distance and speeds of the train in given circumstances. We here discuss some of the basic ideas on how to solve these problems quickly.

**Formula**

**How to Convert kmph into mps**

**How to Convert mps into kmph**

__Example 1____A train running at the speed of 60 kmph crosses a pole in 9 seconds. What is the length of the train?__

The speed of the train, s

= 60 kmph

= 60 × 5/18

= 50/3 mps

Time taken, T

= 9 s

The length of the train, L

= s × t

= 50/3 × 9

= 150 m

__Example 2____A train is moving at a speed of 132 kmph. If the length of the train is 110 meters, how long will it take to cross a railway platform of 165 meter long?__

The speed of the train, S

= 132 kmph

= 132 × 5/18

= 220/3 mps

The length of the train, 𝐿1

= 110 m

The length of the platform, 𝐿2

= 165 m

Time taken, T

= (𝐿1+𝐿2)/S

= (110+168)/(220/3)

= 3.8 m

**Example**

**3**

__A 300 meter long train crosses a platform in 39 seconds while it crosses the signal pole in 18 seconds. What is the length of the platform?__

The length of the train, 𝐿1

=300 𝑚

Time taken to crosses the pole, 𝑇1

=18 𝑠

The speed of the train, S

= 300/18 mps

Time taken to crosses the platform, 𝑇2

= 39 s

The length of the platform, 𝐿2

= 𝑇2× S

= 39 × 300/18

= 650 m