Problems on Trains Tips and Tricks for Government Exams

Theory

• Similar to the concept of speed, distance and time, train problems are specifically based on evaluating the speed, distance covered and time is taken by a train under different conditions. 
• There are specific formulas which are to be used to find answers to the train-based questions and candidates must memorise them in order to crack the answer for problems on trains.
  

Formula

• 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)

Types 

• 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 

Tips

• In train based problems, their are two objects. First object is the Train itself and second object is that, which is crossed by the train.
• So, if a train moving or cross a pole, then the first object is train and the second object is pole.
• If the train moving or cross the platform then the first object is train and second object is platform which the train is crosses.
• And, if a train cross or moving a man or woman who is standing on platform then the train is first object and the second object is that man or woman.
• And also, if a train crossing or moving another train in the same direction or opposite direction then the first object is first train and second object is second train.

Solved Examples