Learn and practice Problems on train with easy explaination and shortcut tricks. All questions and answers on train covered for various Competitive Exams

Solve Problems:

1) A train moving at speed of 90 km/hr crosses a pole in 7 seconds. Find the length of the train.

Length of the train is equal to the distance covered by train to cross the pole. So, we will find the distance travelled by the train in 7 seconds by applying the following formula:

Distance= Speed x Time

Speed is given in Km/hr so we will convert it into m/s as answers are given in meters.

Speed=90* 5/18 = 25 m/s

Time = 7 seconds

Distance = 25 * 7= 175 meters

2) A train of length 200 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

When the train and man are moving in same direction then relative speed will be the difference between their individual speeds. In this problem the other way to find the relative speed is to divide the distance covered (length of train) by the time taken by the train to cross the man.

Relative Speed=200/10

We will convert it into Km/hr

200/10 * 18/5 = 72 km/hr

Now, let the speed of the train is X km/hr. So, the relative speed, 72 km/hr = X km/hr – 10 km/hr

X-10=72

X= 72+10

X= 82 km/hr

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3) A train moving at 50 km/hr crosses a bridge in 45 seconds. The length of train is 150 meters. Find the length of the bridge.

In this problem, both the train and man are moving so we will find the relative speed of the train. They are moving in the same direction, so the relative speed = (speed of train – speed of man)

Relative Speed = (70-10) = 60 km/hr

Relative Speed in m/s = 60* 5/18 = 50/3 m/s

Distance covered to cross the man = length of the train (100 meters)

Time= Distance covered /speed

Time=100/(50/3)

=100* 3/50

= 6 seconds

6) A train of length 200 meters is moving at a speed of 80 km/hr. In what time it will cross a man who is running at 10 km/hr in opposite direction of the train?

In this problem, both the train and man are in motion so we will find the relative speed of the train. They are moving in the opposite direction, so the relative speed = (speed of train + speed of man)

Relative Speed: (80+10) = 90 km/hr

Relative Speed in m/s= 90*5/18 = 225/9 m/sĀ

Distance covered to cross the man = length of the train (200 meters)

Time =200/(225/9)

= 200* 9/225

= 8 seconds

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7) Two trains of length 140 meters and 166 meters are moving towards each other on parallel tracks at a speed of 50 km/hr and 60 km/hr respectively.In what time the trains will cross each other from the moment they meet?

In this problem, both the trains are moving so we will find the relative speed of the train. They are moving in the opposite direction, so the relative speed will be sum of their individual speeds.

Relative speed: (50+60) = 110 km/hr

Relative speed in m/s = 110 *5/18 = 275/9

Distance covered is equal to the sum of the length of trains: 140 + 166= 306 meters

Time =306/(275/9)

= 306*9/275= 10 seconds

8) Two trains of length 120 meters and 140 meters are moving in the same direction on parallel tracks at speed of 82 km/hr and 64 km/hr. In what time the first train will cross the second train?

In this problem, both the trains are in motion so we will find the relative speed of the train. They are moving in the same direction, so the relative speed is equal to the difference of their individual speeds.

Relative Speed: (82-64) = 18 km/hr

Relative Speed in m/s: 18*5/18= 5 m/s

Distance covered is equal to the sum of the length of trains: 120+140 = 260 meters

Time =260/5= 52 seconds

9) A train of length 200 meters takes 12 seconds to cross a man who is running at a speed of 10 km/hr in opposite direction of the train. What is the speed of the train?

The train and man are moving in opposite direction so the speed of train relative to man is the sum of their individual speeds.

Let the speed of train is X km/hr

Then the relative speed will be: (X + 10) km/hr

In this problem the other way to find the relative speed is to divide the distance covered (length of train) by the time taken by the train to cross the man.

Relative Speed =200/12 =50/3

Relative Speed in Km/hr = 50/3 * 18/5= 60 km/hr

Now, X+10 = 60

X= 60 ā 10= 50 km/hr

10) Two trains running in opposite direction cross a man standing on the platform in 36 seconds and 26 seconds respectively. The trains cross each other in 30 seconds. What is the ratio of their speeds?

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