# Shortcut Tips and Tricks on Problems of Trains

Problems on trains and ‘Time and Distance’ are almost same. The only difference is we have to consider the length of the train while solving problems on trains.

Take a quiz : Problems on Trains : Quantitative Aptitude Test

Points To Remember

1. Time taken by a train of length of L meters to pass a stationary pole is equal to the time taken by train to cover L meters.
2. Time taken by a train of length of L meters to pass a stationary object of length P meters is equal to the time taken by train to cover (L + P) meters.
3. If two trains are moving in same direction and their speeds are x km/h and y km/h (x > y) then their relative speed is (x – y) km/h.
4. If two trains are moving in opposite direction and their speeds are x km/h and y km/h then their relative speed is (x + y) km/h.

Unit Conversion

Some Shortcut Methods
Rule # 1:
If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s (x > y) respectively then time taken by the faster train to overtake slower train is given by

Rule # 2:
If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by

Take a quiz : Problems on Trains : Quantitative Aptitude Test

## Few more tips and tricks:

1. When a train passes a stationary point, the distance covered (in the passing) is the length of the train.

2. If the train is crossing a platform or a bridge, the distance covered by the train is equal to the length of the train plus the length of the platform or a bridge.

3. If two trains pass each other ( traveling in the same direction or in opposite directions) , the total distance covered ( in the crossing/ overtaking as the case may be) is equal to the sum of the lengths of the two trains.

4. If two bodies are moving in the same direction at speeds S1 and S2 respectively, then the relative speed is:

Relative speed = S1 – S2

5. If two bodies are moving in opposite direction at speeds S1 and S2 respectively, then the relative speed is:

Relative speed = S1+ S2

6. Two trains of length ‘p’ m and ‘q’ m respectively run on parallel lines of rails. When running in the same direction the faster train passes the slower one in ‘a’ seconds, but when they are running in opposite directions with the same speeds as earlier, they pass each other in ‘b’ seconds. Then,

Speed of the faster train = [( p + q)/ 2] x [ ( a+b) / (a x b)]

Speed of the slower train = [(p-q) / 2] x [ (a-b) / (a x b)]

Note : The speeds obtained using the above formula are in m/ sec, if the speeds are to be expressed in km/h, they have to be multiplied by 18/5.

7. If a train passes by a stationary man in ‘p’ seconds and passes by a platform / bridge, the length of which is ‘m’ m, completely in ‘q’ sec. Then

Length of the train = (m x p) / (q-p).