# Problems on Trains

Train problems are specifically based on evaluating the speed, distance covered and time is taken by a train under different conditions.

### Questions Types on Train Problems

- Time Taken by Train to Cross any stationary Body or Platform – Question may be asked where the candidate has to calculate the time taken by a train to cross a stationary body like a pole or a standing man or a platform/ bridge
- Time Taken by 2 trains to cross each other – Another question that may be asked is the time two trains might take to cross each other
- Train Problems based on Equations – Two cases may be given in the question and the candidates will have to form equations based on the condition given

###### Important Points

- When two trains are going in the same direction, then their relative speed is the difference between the two speeds.
- When two trains are moving in the opposite direction, then their relative speed is the sum of the two speeds.
- When a train crosses a stationary man/ pole/ lamp post/ sign post- in all these cases, the object which the train crosses is stationary and the distance travelled is the length of the train.
- When it crosses a platform/ bridge- in these cases, the object which the train crosses is stationary and the distance travelled is the length of the train and the length of the object.
- When two trains are moving in same direction, then their speed will be subtracted.
- When two trains are moving in opposite directions, then their speed will be added.
- In both the above cases, the total distance is the sum of the length of both the trains.
- When a train crosses a car/ bicycle/ a mobile man- in these cases, the relative speed between the train and the object is taken depending upon the direction of the movement of the other object relative to the train- and the distance travelled is the length of the train.

### Important Formulas to Solve Questions on Train Problems

- Speed of the Train = Total distance covered by the train / Time taken
- If the length of two trains is given, say a and b, and the trains are moving in opposite directions with speeds of x and y respectively, then the time taken by trains to cross each other = {(a+b) / (x+y)}
- If the length of two trains is given, say a and b, and they are moving in the same direction, with speeds x and y respectively, then the time is taken to cross each other = {(a+b) / (x-y)}
- When the starting time of two trains is the same from x and y towards each other and after crossing each other, they took t1 and t2 time in reaching y and x respectively, then the ratio between the speed of two trains = √t2 : √t1
- If two trains leave x and y stations at time t1 and t2 respectively and travel with speed L and M respectively, then distanced from x, where two trains meet is = (t2 – t1) × {(product of speed) / (difference in speed)}
- The average speed of a train without any stoppage is x, and with the stoppage, it covers the same distance at an average speed of y, then Rest Time per hour = (Difference in average speed) / (Speed without stoppage)
- If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken by them to cross each other if the train is moving in opposite direction = (2×t1×t2) / (t2+t1)
- If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken by them to cross each other if the train is moving in the same direction = (2×t1×t2) / (t2-t1)