Quantitative Aptitude - Problems on Trains

Problems on Train

Important Formulae

1)      Speed                    =          Distance/Time

2)      Time                     =          Distance/Speed

3)      Distance                =          Speed x Time

4)      x km/h to m/s       =          x * (5/18) m/s

5)      x m/s to km/h       =          x * (18/5) km/h

6)      If the ratio of the speeds of A and B is a:b then the ratio of times taken by A and B to cover the same distance is b:a

7)      If a man covers equal distances at x km/h and y km/h respectively, then the average speed for the whole journey will be 2xy/(x+y)

8)      If a man covers a distance in equal intervals of time at speeds X₁ km/h, X₂ km/h … X_n., then the average speed for the whole journey will be (X₁+X₂+…)/n .

9)      Time taken by a train of length/metres to pass a pole or a standing man or a signal post is the time taken by the train to cover/metres.

One pole = speed = D/t (length of the train).

10)  Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l+b) metres

Distance/Time      Distance = (l+b).

11)  If two trains of length a metres and b metres cross each other in opposite directions at velocity u m/s and v m/s, then the time taken by the two trains to cross each other will be

Time = (a+b)/(u+v)

12)  If two trains of length a metres and b metres cross each other in opposite directions at velocity u m/s and v m/s, then the time taken by the faster trains to cross the slower train will be

Time = (a+b)/(u-v)

13)  Relative Velocity of two trains with velocity u m/as and v m/s moving in opposite directions will be (u+v) m/s

14)  Relative Velocity of two trains with velocity u m/s and v m/s moving in the in the same direction, u>v, will be (u-v) m/s.

15)  Relative Velocity of two trains with velocity u m/s and v m/s moving in the in the same direction, v>u, will be (v-u) m/s.