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**Important Aptitude formulas, shortcut methods and tricks on Trains Problems:**

**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**