## Problems on Train Formula and shortcut tricks

It is necessary for the candidates who are going to appear in the Bank and Railway exams must know the Problems on Train Formula and the short tricks. In many competitive exams, questions related to speed of train, time taken by train and distance covered by train are generally asked by the examiner. It looks easy but if the candidate does not know about the shortcut tricks and formulas then he/she took too much time to solve it. We are providing some examples on Problems on train formula and short cut tricks that will surely helpful for you.

If you keep practicing the formulas daily then you will easily complete the section in the examination. Don’t just read the formulas; write the formulas in your notebooks so that you will remember this at the time of examination. In many exams a common problem is always there i.e. time issue. The given time is less as compared to the no. of questions asked so it is very difficult to solve the paper in a given period of time. But with the help of shortcut tricks and train formulas you can complete your paper in a given time. Aslo stay connected with us through our web portal www.privatejobshub.in and get other maths preparation material related to this.

### Problems On Train Formulas

The problem on trains is one of the scoring chapters in competitive exam papers. Three things you just need to keep in mind i.e. speed, distance and time of the train. The other two important things should be kept in mind i.e. first is train and the other is that which is crossed by the train.

This type of problems on train is given in Quantitative Aptitude section which is very important topic in Bank/SSC/PSC/Railwayexam. Some examples are given below for your practice:

 Train speed = Distance/time

To change km/hr into m/s, we convert it by multiply by 5/18.

Example: 90 km/hr means to say 90 X 5/18 = (5X5) = 25 m/s.

We can convert m/s into km/hr multiply by 18/5.

Example: 90 m/s means to say 90 X 18/5 = (18X18) = 324 km/hr.

Some Important Facts
• There are train based problems on two objects, first is train and second object is that which is crossed by the train.
• If a train moving or cross a pole then the first object is train and the second object is pole.
• If ‘A’ train crossing or moving another train in the same direction or opposite direction than the first object is first train and the second object is second train.
Shortcut Tricks for Bank/SSC/PSC/Railway Exam

Time is the main factor in competitive exams. If you know how to manage time then you will surely do great in Bank/SSC/PSC/Railway Exam. For this you need to remember the formulas and shortcut tricks. We try to provide all types of shortcut tricks on problems on time taken by train, problem on speed of train and problems on train running in same and opposite directions.

Problem On Time Taken By Train

Shortcut tricks on time taken by train are one of the most important topics in exams. Some examples on time taken by train shortcut tricks are given below:

Example: A train 480 meter long running at the speed of 54 km/hr. In what time will it pass a bridge 120 meter long?

Answer: Total distance covered = (480 + 120) meter = 600 meters.
Speed = (54 X 5/18) = 15 m/s.
Required time = (600/15) sec = 40 sec.

Example: A mail train 250 meters long passes a standing boy in 5 seconds.  How long will it take to cross a bridge 500 meters long?

Answer: Train length = 250 meters
(250/5) m/s = 50 m/s.
Time taken to cross its own length is 50 m/s.
Time taken to cross the bridge = (500 + 250/50) m/s = 750/50 = 15 m/s.

Problem On Speed Of Train

Some examples on speed of train shortcut tricks are given below:

Example: A 270 m long train passes a bridge thrice its length in 30 sec. find the speed of the train in km/hr.

Answer: 270 X 3 + 270 /30 = 1080/30
36X 18/5 = 129.6 km/hr.

Example: A 720 meter long train crosses a man standing in 60 seconds. What would be the speed of the train?

720/60 = 12 m/sec.

Example: A super fast train 140m long crossing a long tunnel of 450m in 20 sec. What would be the speed of train?

Answer: Speed = distance 1 + distance 2 / Time
140+450 = 590/20 = 29.5 m/s.

Example: A local train 150 m long passes a boy, and running at 3 km/hr in the same direction, in 10 seconds. What would be the speed of the train?

Answer: Speed of the train relative to man =150 / 10 m/sec = 15 m/sec
Convert meters to km=15 x 18 / 5 = 54 km/hr.
Let the speed of the train be x km/hr
x – 3 = 54
x = 57 km/hr.

Example: A bus passes a distance of 750 km. in 15 hrs. What would be speed of the bus?

Speed = 750/ 15 = 50 km/hrs.

Problem On Train Running Same Direction

Some examples on Train running in same direction shortcut tricks are given below:

Example: A train is 250 m long is running with the speed of 65 km/hr, a man running at 5 km/hr in same direction in which the train is moving, find what time will it pass a man.

Answer: if direction is given in the same direction then we subtract it (65-5) = 60 km/hr.
Convert it into m/s using 60 X 5/18 = 50 /3 m/s.
If the time taken to passing the man who running, that is 50/3 m/s.
So, we can easily get the distance of m/s.
It cover 250 m that is = 250 X 3/50 = 15 sec.
So, the train time taking to cover the distance is 15 sec.

Example: Two super fast train 180 meters and 180 meters in length respectively are running in same directions, one at the rate of 58 km and the other at the rate of 50 km an hours. What time will they be cross of each other?

Answer: Two fast trains are running is same direction and their relative speed is = 58 – 50 = 8 km / hours.
8 x 5/18 = 20 / 9 m/sec.
Total length of both train is (180 + 180) = 360 meters.
So, the required time is = Total length / Relative speed = (180 + 180) x 9 / 20 = 360 x 9 / 20 = 162 sec.
Problem On Train Running Opposite Direction

Some examples on Train running opposite direction shortcut tricks are given below:

Example: 180 m and 120 m Mail train are running on parallel in an opposite direction at the speed of 67 km/hr and 77 km/hr respectively. Find when they cross each other?

Answer: (67 + 77) X 5/18 = 180 + 120/Time
Time = 15 / 2 sec.

Example: Two super fast trains 180 m and 180 m in length respectively are running in opposite directions, one at the rate of 58 km and the other at the rate of 50 km an hrs. What time will they be completely clear of each other from the moment they met?

Answer: Two fast trains are running in opposite direction and their relative speed = 58+50 = 108 km/hrs.
So the two trains met each other at 108 km/hrs.
108 X 5/18 = 30 m/s.
So, the required time = Total length / Relative speed = 180 + 180 /30 = 12 sec.

Example: 170 meter and 130 meter long two super fast train are running in opposite direction at speed of 52 km/hr and 56 km/hr in par-allay. In What time would be they cross each other?

Answer: Convert speed km/hr to m/sec = 52 + 56 = 108 x 5 / 18 = 30 m/sec.
Time = distance / speed = 170 + 130 / 30 = 300 / 30 = 10 sec.
So, they cross each other after 10 seconds.

Problem on finding length of train or platform

Some examples on Problem on finding length of train or platform shortcut tricks are given below:

Example: 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/s.
30 = 120 + x/18
120 + x = 540
X = 540 – 120 = 420.

Example: A metro rail is running at a speed of 90 km/hr. If crosses a platform whose length is twice that of train in 36 sec. What is the length of the platform in meter?

Answer: Speed = 90 X 5/18 = 25 m/s.
25 = x + 2x /36
X = 300 m.
Length of platform = 300 X 2 = 600 meter.

 Take a Test  Now

Example: An express train passes a tunnel in 21 sec whose length is 130 m long moving with speed of 90 Km / hr. what is the length of tunnel?

Answer: Let length be the x meters.
We know the conversion of Km/hr to m/sec is = 90 x 5 / 18 = 25 m/sec
25 = 130 + x / 21
130 + x = 25 x 21
x = 525 – 130
x = 395
So length is the 395 meters.

Example: An 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.

 Check Some Other Essential Maths Formulas Links

Example: An 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.