Problems on Trains – Quantitative Aptitude Notes

Speed Formula

Speed = Distance / Time 

Unit Conversion

Convert from km/hr to m/sec:

x km/hr = x (5/18) m/sec

Convert from m/sec to km/hr

x m/sec = x (18/5) km/hr

Ratio of Speeds

If the ratio of speeds of A and B is a:b, then the ratio of time taken by them is 1/a:1/b or b:a.

Average Speed

Suppose a train covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during whole journey is 2xy / (x+y).

Relative Speed between two trains

Relative Speed gives the speed of trains with respect to each other.

1. Two trains travelling in the same directions at x & y speeds (x>y), then their relative speed will be x-y.
2. Two trains travelling in opposite directions at x & y speeds, then their relative speed will be x+y.

Train Crossing Problems

1. The time taken by a train of length L to pass a point or observer is equal to the time taken by the train to cover distance L.
   • Time taken by train to cross a point = Length of train/speed of train
2. The time taken by a train of length L to pass an object(e.g. platform) of length B is equal to the time taken by the train to cover distance L+B.
   • Time taken by train to cross an object = (Length of train + Length of object)/speed of train
3. The time taken to cross another train.
   • Time taken to cross another train = (Sum of Length of both trains)/(Relative Speed between the trains)