Problems on Trains - Quantitative Aptitude for Government Exams

Train problems form an integral part of the time and speed questions which are frequently asked in the quantitative aptitude section of various Government exams. These questions are different from the basic speed, distance and time questions and require a different approach to be answered.

Mostly the number of questions asked from the train problems topic varies between 1-3 and are mostly asked in the word problems format. 

Aspirants who wish to know the other topics which are a part of the quantitative aptitude section, along with the exams in which this section is included and sample questions, can visit the linked article.

Table of Contents:

  1. Problems on Train – Basic Concept
  2. Types of Questions on Train Problems
  3. Important Formulas
  4. Tips and Tricks to Solve Train Problems
  5. Problems on Train – Sample Questions

With the increased competition and the level of exam, it is important that a candidate gives equal attention to the preparation of every single topic in order to ace the examination.

So, for candidates assistance, we have discussed in detail the concept of train-based problems, important formulas related to the same, tips to solve the questions easily and efficiently, along with some sample questions to prepare.

Aspirants are free to check the various other quantitative aptitudes related topics and articles given below:

Number Series Data Sufficiency Data Interpretation
Problems on Ages Boat and Stream Shortcut Tricks for Square, Cube & Multiplication

Problems on Train – Basic Concept

Similar to the concept of speed, distance and time, train problems are specifically based on evaluating the speed, distance covered and time is taken by a train under different conditions. 

The weightage of questions asked from this topic in the quantitative aptitude section of various Government exams is mostly between 1-3 marks and the common exams which include this topic in their syllabus are Bank, Insurance, SSC, RRB and other major Government exams.

There are specific formulas which are to be used to find answers to the train-based questions and candidates must memorise them in order to crack the answer for problems on trains.

Interested candidates can also check the 10 Simple Maths Shortcuts and Tricks to ace the quantitative aptitude section at the linked article.

Given below are the links with the detailed syllabus for various competitive exams for the reference of candidates:

Bank Exam Syllabus SSC Syllabus RRB Syllabus
FCI Syllabus LIC Syllabus UPSC CAPF Syllabus

Types of Questions on Train Problems

Over the years, the exam pattern has changed with the increase in the number of applicants and every year candidates notice a new pattern or format in which questions are asked for various topics in the syllabus.

It is important that a candidate is aware of the types in which a question may be framed or asked in the examination to avoid any risk of losing marks.

Thus, given below are the type of questions which may be asked from the train-based problems:

  1. Time Taken by Train to Cross any stationary Body or Platform – Question may be asked where the candidate has to calculate the time taken by a train to cross a stationary body like a pole or a standing man or a platform/ bridge
  2. Time Taken by 2 trains to cross each other – Another question that may be asked is the time two trains might take to cross each other
  3. Train Problems based on Equations – Two cases may be given in the question and the candidates will have to form equations based on the condition given 

Aspirants must also refer to the important pointer given below for the Train problems.

The image given below mentions the basic points a candidate must remember in order to answer the train based word problems:

Problems on Trains - Quantitative Aptitude for Government Exams

Important Formulas

To solve any numerical ability question a candidate needs to memorise the related formulas to be able to answer the questions easily and efficiently.

Given below are the important train-based questions formulas which shall help candidates answer the questions based on this topic:

  • Speed of the Train = Total distance covered by the train / Time taken
  • If the length of two trains is given, say a and b, and the trains are moving in opposite directions with speeds of x and y respectively, then the time taken by trains to cross each other = {(a+b) / (x+y)}
  • If the length of two trains is given, say a and b, and they are moving in the same direction, with speeds x and y respectively, then the time is taken to cross each other = {(a+b) / (x-y)}
  • When the starting time of two trains is the same from x and y towards each other and after crossing each other, they took t1 and t2 time in reaching  y and x respectively, then the ratio between the speed of two trains = √t2 : √t1
  • If two trains leave x and y stations at time t1 and t2 respectively and travel with speed L and M respectively, then distanced from x, where two trains meet is = (t2 – t1) × {(product of speed) / (difference in speed)}
  • The average speed of a train without any stoppage is x, and with the stoppage, it covers the same distance at an average speed of y, then Rest Time per hour = (Difference in average speed) / (Speed without stoppage) 
  • If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken by them to cross each other if the train is moving in opposite direction = (2×t1×t2) / (t2+t1)
  • If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken by them to cross each other if the train is moving in the same direction = (2×t1×t2) / (t2-t1)

Other related links to prepare for Government exams have been given below for your reference:

Preparation tips for Quantitative Aptitude for Bank Exams Quantitative Aptitude Preparation tips for IBPS PO Important Maths Questions for SBI PO 
IBPS PO Prelims Quantitative Aptitude Syllabus Logical Reasoning Syllabus General English for Competitive Exams

Tips and Tricks to Solve Train Problems

To assist aspirants to prepare for and ace the quantitative aptitude section, given below are a few tips which may help you answer the train problems quicker and more efficiently:

  • Always read the question carefully and do not haste in answering it as the train-based questions are usually presented in a complex manner
  • Once you read the question, try to apply a formula in them, this will may solution direct and save you some time
  • Do not guess if you are not sure. Since there is negative marking in competitive exams, ensure that you do not make assumptions and answer the questions
  • Do not over complicate the question and spend too much time on solving it if you are not able to answer
  • In case of confusion, you can also refer to the options given in the objective type papers and try finding the answer with the help of options given 

Candidates can refer to the below-mentioned links and solve more and more mock tests, question papers and practise papers to apprehend the level of the exam better:

Problems on Train – Sample Questions

Try solving the sample questions given below based on Train problems and practise more to score more in the upcoming Government exams.

Q 1. A train running at the speed of 56 km/hr crosses a pole in 18 seconds. What is the length of the train?

  1. 200m
  2. 250m
  3. 325m
  4. 280m
  5. 140m

Answer: (4) 280m


Speed = {56 × (5/18)} m/sec = (140/9) m/sec

Length of the train (Distance) = Speed × Time = {(140/9) × 18} = 280 m

Q 2. Time is taken by two trains running in opposite directions to cross a man standing on the platform in 28 seconds and 18 seconds respectively. It took 26 seconds for the trains to cross each other. What is the ratio of their speeds?

  1. 2:3
  2. 3:2
  3. 1:4
  4. 3:1
  5. 4:1

Answer: (5) 4:1


Let the speed one train be x and the speed of the second train be y

Length of the first train = Speed × Time = 28x

Length of second train =  Speed × Time = 18y

So, {(28x+18y) / (x+y)} = 26

⇒ 28x+18y = 26x+26y

⇒ 2x = 8y

Therefore, x:y = 4:1

Q 3. It takes a 360 m long train 12 seconds to pass a pole. How long will it take to pass a platform 900 m long?

  1. 40 seconds
  2. 32 seconds
  3. 42 seconds
  4. 50 seconds
  5. 72 seconds

Answer: (3) 42 seconds


Speed = (360/12) m/sec = 30 m/sec

Required Time = {(360+900) / 30} = 1260 / 30 = 42 seconds

Q 4. A train 300 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 150 m long?

  1. 32 seconds
  2. 30 seconds
  3. 51 seconds
  4. 16 seconds
  5. 10 seconds

Answer: (2) 30 seconds


Speed = {54 × (5/18)} m/sec = 15 m/sec

Total distance which needs to be covered = (300+150)m = 450m

Time = Distance/Speed

Required Time = 450 / 15 = 30 seconds

Candidates must also practise more questions to understand the topic even better and to be able to answer any question from this topic if asked in the final examination.

Given below are a few other preparation links for your assistance:

Daily Current Affairs Static GK Banking Awareness
SSC General Awareness Computer Fundamentals Bank Exams

For any further details regarding the competitive exams, candidates can turn to BYJU’S and get the study material or preparation tips.

Government Exam 2023


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