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    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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    Item Reviewed: Important Aptitude formulas on Trains Rating: 5 Reviewed By: Pranab Debnath
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