Hi aspirants,

Questions on trains have been a frequent occurrence in SSC exams till 2016, so we know that in SSC CGL 2017, every candidate can easily solve two questions of this topic in quantitative section successfully with the help of a few simple hacks.

All you need to remember is the direction of train in which it cross the object along with speed, time and distance. The train based problems based on two things: Train and the object which is crossed by the train.

Points To Remember While Solving Problems On Trains

  1. Time taken by a train of length of L meters to pass a stationary pole is equal to the time taken by train to cover L meters.
  2. Time taken by a train of length of L meters to pass a stationary object of length P meters is equal to the time taken by train to cover (L + P) meters.
  3. If two trains are moving in same direction and their speeds are x km/h and y km/h (x > y) then their relative speed is (x – y) km/h.
  4. If two trains are moving in opposite direction and their speeds are x km/h and y km/h then their relative speed is (x + y) km/h.

Unit Conversion – kmph ⇔ mps

km/h to m/sec conversion

m/sec to km/h unit conversion

Shortcut Methods For Trains

Rule 1:
If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s (x > y) respectively then time taken by the faster train to overtake slower train is given by

Trains quantitative aptitude shortcuts

Example:

Two trains of length 130 meter and 70 meter are running in the same direction with the speed of 50 km/h and 70 km/h. How much time will faster train take to overtake the slower train from the moment they meet?
Sol:

Let’s say p = 130 meter = 0. 13 km
q = 70 meter = 0.07 km
x = 70 km/h and y = 50 km/h,
So from the equation given above,

Trains shortcut methods

0.01 hours = 36 second
So it will take 36 seconds to overtake.

Rule 2:
If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by

Trains Shortcuts

Example:

Two trains of length 130 meter and 70 meter are running in the opposite direction with the speed of 50 km/h and 70 km/h. How much time will trains take to cross each other from the moment they meet?
Sol:

Let’s say p = 130 meter = 0. 13 km
q = 70 meter = 0.07 km
x = 70 km/h and y = 50 km/h,
So from the equation given above,

Trains quantitative aptitude

0.0017 hours = 6 seconds
So it will take 6 seconds to cross each other.

Example 1:  A 120 m long train passes a bridge in 18 sec, moving with a speed of 108 km/hr. What would be the length of the bridge ?

Answer : Speed = 108 x 5 / 18 = 30 m/sec.

30 = 120 + x / 18

120 + x = 540

x = 540 – 120 = 420

Example 2:

A Express train is running at speed of 90 Km / hr. It crosses a bridge whose length is twice that of train in 36 seconds. What is the length of bridge in meter ?

Answer :

At First we convert the speed into 90 Km / hr = 90 x 5/18 = 25 m /sec.

now here is suppose the train length is x so bridge length is 2x.

according to question

25 = x + 2x / 36

x = 300 m.

length of platform is 300 x 2 = 600 m.

So length of bridge is 600 meter.

Example 3:

A Express train passes by a shop boy standing on the platform in 9 seconds and passes by the platform completely in 27 seconds. If the length of the platform is 350 meters, What is the length of the train ?

Answer :

Let the length of the train be x meters.                                                                                            Then speed of the train = x / 9 meters / sec.                                                                                       And also the speed of the train = x + 350 / 27 meters / sec.                                                                 Both the speed should be equal, i e, x /9 = x + 33 / 27.                                                                             or, 27x – 9x = 9 x 350

  x = 9 x 350/ 18 = 175 meters.

Shortcut tricks :

Length of train = Length of platform / Difference in time x Time taken to cross a shop or man.

= 350 x 9 / 18 = 150 meters.

Example 4: A Local train crosses a bridge in 30 seconds. If the length of the local train is 300 m. then find what is the length of the bridge ?

Answer : To find length of platform, we need in this question the speed of local train which has not given, we can’t determined.

Example 5: A bike travel a journey in 13 hrs. The 1st half at 24 km/hr and the 2nd half at 28 km/hr, Find the distance of the journey.

Answer : Let the total distance be X

( X / 2 / 24 ) + ( X / 2 / 24) = X / 48 + X / 56                                                                                               =>     7X + 6X / 336 = 13                                                                                                                                       =>      13X / 336 = 13                                                                                                                                             =>     X = 4368 / 13 =  336

Hope this was helpful.

Happy Learning !!

-Team SSCHacks

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