**Problems on Trains with Solutions :**

In this section, we will learn, how to solve problems on trains step by step.

Before look at the problems on trains, if you would like to know the shortcuts which are required to solve problems on trains,

**Problem 1 :**

If the speed of a train is 20 m/sec, find the speed the train in kmph.

**Solution :**

Speed = Distance / Time

Speed = 20 m/sec

Speed = 20 x 18/5 m/sec

Speed = 72 kmph

Hence, the speed of the train is 72 kmph.

**Problem 2 :**

The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform.

**Solution :**

Distances needs to be covered to cross the platform is

= Sum of the lengths of the train and platform

So, distance traveled to cross the platform is

= 300 + 500

= 800 meters

Time taken to cross the platform is

= Distance / Speed

= 800 / 20

= 40 seconds

Hence, time taken by the train to cross the platform is 40 seconds.

**Problem 3 :**

A train is running at a speed of 20 m/sec.. If it crosses a pole in 30 seconds, find the length of the train in meters.

**Solution :**

The distance covered by the train to cross the pole is

= Length of the train

**Given :** Speed is 20 m/sec and time taken to cross the pole is 30 seconds

We know,

Distance = Speed ⋅ Time

So,

length of the train = Speed ⋅ Time

Length of the train = 20 ⋅ 30

Length of the train = 600 meters

Hence, length of the train is 600 meters.

**Problem 4 :**

It takes 20 seconds for a train running at 54 kmph to cross a platform.And it takes 12 seconds for the same train in the same speed to cross a man walking at the rate of 6 kmph in the same direction in which the train is running. What is the length of the train and length of platform (in meters).

**Solution :**

Relative speed of the train to man = 54 - 6 = 48 kmph

= 48 ⋅ 5/18 m/sec

= 40/3 m/sec

When the train passes the man, it covers the distance which is equal to its own length in the above relative speed

**Given :** It takes 12 seconds for the train to cross the man

So, the length of the train = Relative Speed x Time

= (40/3) ⋅ 12

= 160 m

Speed of the train = 54 kmph

= 54 ⋅ 5/18 m/sec

= 15 m/sec

When the train crosses the platform, it covers the distance which is equal to the sum of lengths of the train and platform

**Given :** The train takes 20 seconds to cross the platform.

So, the sum of lengths of train and platform

= Speed of the train ⋅ Time

= 15 x 20

= 300 meters

That is,

Length of train + Length of platform = 300

160 + Length of platform = 300

Length of platform = 300 - 160

Therefore, length of platform = 140 meters

Hence the lengths of the train and platform are 160 m and 140 m respectively.

**Problem 5 :**

Two trains running at 60 kmph and 48 kmph cross each other in 15 seconds when they run in opposite direction. When they run in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. Find the length of the two trains (in meters).

**Solution :**

When two trains are running in opposite direction,

relative speed = 60 + 48

= 108 kmph

= 108 ⋅ 5/18 m/sec

= 30 m/sec

Sum of the lengths of the two trains is sum of the distances covered by the two trains in the above relative speed.

Then, sum of the lengths of two trains is

= Speed ⋅ Time

= 30 ⋅ 15

= 450 m

When two trains are running in the same direction,

relative speed = 60 - 48

= 12 kmph

= 12 ⋅ 5/18

= 10 / 3 m/sec

When the two trains running in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds.

The distance he covered in 36 seconds in the relative speed is equal to the length of the slower train.

Length of the slower train = 36 ⋅ 10/3 = 120 m

Length of the faster train = 450 - 120 = 330 m

Hence, the length of the two trains are 330 m and 120 m.

Apart from the problems given above, if you need more problems on trains, please click the following links.

**Problems on Trains with Solutions - 1**

**Problems on Trains with Solutions - 2**

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems on trains.

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