If you are practising to ace **competitive exams** like **GRE** or **GMAT **then **logical reasoning** is one section that you really need to focus on. Logical reasoning is a part of almost every competitive exam and students usually have a hard time solving that section of the question paper but with correct tricks and proper guidance and practice, you can easily solve that section in no time. Problems on trains are among the popular examination questions, every entrance exam usually has a few questions that involve problems related to trains, their speed, direction, and length. This blog will try to simplify and explain this section of the paper in order to give you a basic idea of how to go about problems on trains.

## Problems on Trains: Concepts and Logics

The problems on trains follow a certain format that revolves around some fundamental concepts, these are:

#### Distance and time

The question based on trains usually includes concepts like relative motion, speed and time. If you are good in physics or even if you remember the basic concepts of it then you can easily ace this section. There are questions that involve distance and time. One formula that you need to keep in mind is *d= st, *where *d *is distance, *s *is the speed and *t *stands for time. Let’s look at a question which involves this formula:

**Question**: Train A travels at 50 mph, Train B travels at 70 mph. Taking into account that both trains leave the station at the same time, evaluate how far apart they will be after two hours?

**Solution**: To calculate the distance here you need to add the distance traveled by both the trains together.

Distance traveled by train A will be: d=*s*t, the rate at which it travels here is 50mph and the time is 2 hours.

So the distance traveled by train A will be 50×2 = 100.

Similarly, distance traveled by train B will be 70×2 = 140.

Now if we add the distances 140+100= 240, hence the distance at which they travel apart from each other would be 240 miles.

If the trains are traveling in the same direction then we would subtract distances traveled by both the trains i.e. 140-100= 40, then the answer would be 40 miles.

**Length of the train**

In these type of questions, you need to find out the length of the train with the given information in the question. These questions usually include relative speed and the formula used here is the same *d= st. *Let’s look at an example in order to understand the problem more clearly.

**Question**: A train is traveling at a speed of 60kmph it then overtakes a bike that is traveling at 30kmph in about 50 seconds. Now calculate the length of the train.

**Solution**: To calculate the length of the train we need to find out the distance traveled by the train, since the bike is also in motion we need to look at the relative speed of the bike and the train.

Since both the objects are moving in the same direction we need to subtract the distance traveled by both the objects i.e. 60-30= 30, so the relative speed is 30kmph.

Now let’s find out the distance traveled by train while taking over the bike, applying the formula, d= st, distance will be 30kmphx50 seconds. Now let’s convert the distance into meter per second.

1 kmph = 5/18 m/sec

Therefore 30kmph= 30×5/18= 8.33 m/sec

Therefore distance traveled will be 8.33×50= 416.5 meters, the length of the train is 416.5 meters.

## Types of Questions: Problems on Train

The number of applicants has increased throughout the years, and each year, candidates observe a new pattern or format in which questions are asked for various topics in the syllabus.

In order to minimise the chance of receiving a bad grade, candidates should be aware of the several ways questions may be phrased or asked throughout the exam.

As a result, the types of questions that might be posed from train-based challenges are listed below:

**Time Taken by Train to Traverse Any Stationary Body or Platform**– A question may require the applicant to determine the amount of time it takes a train to cross a particular type of stationary object, such as a pole, a standing person, a platform, or a bridge.**Time it takes for two trains to cross paths –**The duration it might take for two trains to cross each other is still another possible inquiry.**Train Equation-Based Problems-**The question may present two situations, and the candidates must build equations based on the conditions.

## Key Formulas For Problems on Train

A candidate must memorise the relevant formulas in order to solve any numerical ability question so they can respond quickly and effectively.

The following key formulas for train-related questions will aid candidates in responding to questions based on this subject:

**Speed of the Train = Total distance covered by the train / Time taken**- The time it takes for two trains to cross each other is equal to (a+b) / (x+y) if the lengths of the trains, say a and b, are known and they are going at speeds of x and y, respectively.
- When the length of two trains, let’s say a and b, is known and they are travelling at speeds of x and y, respectively, in the
**same direction**, the time it takes for them to cross each other is equal to (a+b) / (x-y). - When two trains begin travelling in the same direction from points x and y and cross each other after travelling in opposite directions for times t1 and t2, respectively, the ratio of the speeds of the two trains is equal to t2:t1.
- If two trains depart from stations x and y at times t1 and t2, respectively, and they go at speeds L and M, respectively, then the distance from x at which they will collide is equal to (t2 – t1) (speed product) / (difference in speed).
- When a train stops, it travels the same distance at an average speed of y rather than the normal average speed of x. Hourly Rest Time = (Difference in Average Speed) / (Speed without stoppage)
- If it takes two trains of similar length and speed t1 and t2 to pass a pole, the time it takes for them to cross each other if the trains are going in the opposite direction is equal to (2t1t2) / (t2+t1).
- If it takes two trains of equal length and speed t1 and t2 to cross a pole, the time it takes for the trains to cross each other if they are travelling in the same direction is equal to (2t1t2).

## Things to Keep in Mind While Solving Problems on Trains

While solving the section related to problems on trains it is important to keep certain things in mind to ensure efficiency and accuracy. Here are a few things that you should keep in mind:

- Make sure all the units are the same, if not don’t forget to change them.
- Read the questions carefully and keep in mind the concepts of speed and relative speed.
- Remember the basic formulas
- Be clear about all the concepts.

## FAQs

**How do you solve a train problem in math?**

Always read the question carefully before responding, as train-based topics are frequently given in a convoluted manner. Try to apply a formula after reading the question; this may lead to a quick solution and save you time.

**What is relative speed in train problems?**

When two bodies are moving in the same direction, the relative speed is equal to the difference in their speeds. For example, a person in a train travelling at 60 km/hr in the west will perceive the speed of the other train travelling at 40 km/hr as being 20 km/hr (60-40).

**What is the formula of train?**

x km/h = x*(5/18) m/s. The amount of time needed for a train of length/meters to pass a pole, a single post, or a standing person is equal to the distance the train must go in/meters.

Understanding the concepts behind problems on trains can help you in developing strategies to solve those questions. While we have tried to give you all the important information required to tackle these questions, it is natural to feel stressed about the entrances. The experts at **Leverage Edu **can help you plan for these exams so that nothing comes between you and your dreams.