Important Aptitude formulas on Trains - ObjectiveBooks

# Important Aptitude formulas on Trains

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

If x = length of train
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:
Formula:                Trains Aptitude Formulas
Solved Examples:  Solved Examples: Set 01     Solved Examples: Set 02
Practice Test:         Practice Test: 01     Practice Test: 02
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