### Problems on Trains- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems related to Speed, Distance and Time. Basic knowledge regarding calculating speed, distance and time is important for various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

### Case I: If a train of length L passes a pole or a man with speed S in time T. Then Speed = L / T. {We will take distance covered = Length of the train = L}

Eg 1: A train 200 m long is running at the speed of 40 km/hr passes a pole. Find the time taken by train to cross the pole.
Soln: Speed of the train = 40 km/hr
Distance = 200 m = 0.2 km
Time = Distance / Speed = 0.2/40 = 1/200 hrs = 3600/200 secs = 18 secs

Eg 2: A train moving at speed of 40 km/hr crosses a pole in 18 seconds. Find the length of the train.
Soln: Speed of the train = 40 km/hr
Time = 18 seconds = 18/3600 hrs
Distance = Speed * Time = 40 * (18/3600) = 0.2 km = 200 meters.

### Case II: If a train of length L meter passes a platform or object of length M with speed S in time T. Than Speed = (L+M)/T. {We will take distance as sum of (L + M)}

Eg 1: A train 200 m long running crosses a platform of length 300 m in 36 seconds. Find the speed of the train.
Soln: Speed = (L + M) / T
Speed = (300 + 200) / 36 = 500/36 m/s = (500/36) * (18/5) = 50 km/hr

Eg 2: A train running at the speed of 50 km/hr crosses a platform of length 300 m in 36. Find the length of the train.
Soln: Let speed of the train be L, length of platform = 300 m = 0.3 meter,
Time = 36 sec = 36/3600 = 1/100.
Speed = (L + M) / T
=> 50 = (L + 0.3) / (1/100)
=> L = 0.2 km = 200 meter.

### Time taken = (L1 + L2) / (S1 + S2)

Eg 1: Two trains 200 meter and 300 meter in length are running towards each other on parallel lines, one at speed of 45 km/hr and other at speed of 55 km/hr. In what time will cross each other?
Soln: L1 = 200 meter = 0.2 km, L2 = 300 meter = 0.3 km
S1 = 45 km/hr, S2 = 55 km/hr
Time taken = (L1 + L2) / (S1 + S2) = (0.2 + 0.3) / (45 + 55) = 0.5/100 hr = (0.5/100) * 3600 = 18 secs

### Time taken = (L1 + L2) / (S1 - S2)

Eg 1: Two trains 200 meter and 300 meter in length are running towards each other on parallel lines, one at speed of 45 km/hr and other at speed of 55 km/hr. In what time will cross each other?
Soln: L1 = 200 meter = 0.2 km, L2 = 300 meter = 0.3 km
S1 = 45 km/hr, S2 = 55 km/hr
Time taken = (L1 + L2) / (S2 - S1) = (0.2 + 0.3) / (55 - 45) = 0.5/10 hr = (0.5/10) * 3600 = 180 secs

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