Important Aptitude formulas, shortcut methods and tricks on Trains Problems:
If x =
length of train
And, t = time taken
And, t = time taken
Then,
(1) The
train passes a standing person or pole; velocity, v = x/t
(2) It
passes bridge or platform of length y; velocity, v = (x + y)/t
(3) It
passes a man moving in the direction of train with velocity v’ is; (v - v´) =
x/t
(4) It
passes another train of length y moving in the same direction with a speed v´;
(v - v´) = (x + y)/t
(5) When
trains are moving in opposite direction; (v + v´) = (x + y)/t
(6) If two
trains starts at the same time from two points A and B towards each other and
after crossing, they take time t₁ and t₂ hours in reaching B and A
respectively, then
(Speed of A)/(Speed of B) = (√t₁) /
(√t₂)
(7) Stoppage
= (difference of two speeds/Fastest speed) × 60 min/hr.
(8) Average
of two different speeds x and y, to travel same distance = 2xy/(x + y)
Note
1. km/hr
to m/sec conversion: a km/hr = [a × (5/18)] m/sec.
2. m/sec to km/hr conversion: a m/sec = [a × (18/5)] km/hr.
Example: 01
A person standing on a platform 160 meters
long finds that a train crosses the platform in 54 sec, but himself in 30 sec.
Find the length of the train.
Solution:
Let, x be
the length of the train
Therefore, v
= x/30 …………………eq.(i)
And,
v = x + 160)/54 ……………..eq.(ii)
From,
equation (i) and (ii), we get, x = 200 m.
Example: 02
A train of 24 carriages, each carriage of
60 m length with an engine of 60 m length is running at a speed of 60 km/hr.
Find out the time in which the train will cross the bridge measuring 1.5 km in
length.
Solution:
The length
of the train, x = (24 + 1) × 60 = 1.5 km
Given,
length of bridge, y = 1.5 km and speed, v = 60 km/hr
Therefore,
time t = (x + y)/v = (1.5 + 1.5)/60 = 3/60 hr. = 3 min.Trains Aptitude: Next Tests