Shortcut 50:
Train crossing a pole
$T=\frac{L_T}{S_T}$
Question:
A train of length 450m is travelling at a speed of 54kmph. How long will it take to cross a pole?
Speed of train ST in m/s = 54x(5/18)
= 15mps
Length of train = LT = 450m
Time taken to cross = 450/15
= 30 seconds

Shortcut 51:
Time taken to cross a platform or bridge
$T=\frac{L_T+L_P}{S_T}$
Question:
A train of length 200m crosses a platform of length 150m at a speed of 72kmph. How long will the train take to cross the platform?
LT = 200m
LP = 150m
ST = 72x(5/18) = 20mps
Time taken to cross the platform = (200+150)/20
= 17.5 seconds

Shortcut 52:
Trains crossing another train in opposite direction
$T=\frac{L_1+L_2}{S_1+S_2}$
Question:
Two trains A and B of length 200m and 300 are travelling at a speed of 54kmph and 36kmph respectively in opposite directions. How long will they take to cross each other?
L1 = 200; L2 = 300
S1 = 54kmph = 54(5/18)mps = 15mps
S2 = 36kmph = 36(5/18)mps = 10mps
Substitute the values in the above equation, we get
T = (200+300)/(15+10)
= 20 seconds

Shortcut 53:
Two trains crossing each other in same direction
$T=\frac{L_1+L_2}{S_1\sim S_2}$
Question:
Two trains A and B of length 200m and 300 are travelling at a speed of 54kmph and 36kmph respectively in same directions. How long will they take to cross each other?
L1 = 200; L2 = 300
S1 = 54kmph = 54(5/18)mps = 15mps
S2 = 36kmph = 36(5/18)mps = 10mps
Substitute the values in the above equation, we get
T = (200+300)/(15-10)
= 100 seconds

Shortcut 54:
Train crossing a man on another train in opposite direction
$T=\frac{L_T}{S_1+S_2}$
Question:
Two trains A and B of length 300m and 400 are travelling at a speed of 72kmph and 36kmph respectively in opposite directions. How long will train A take to cross a man travelling in train B?