train problem solving tricks

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Problems on Trains

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.

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:

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:

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:

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
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
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:

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:

Free Online Government Exam Quiz
Bank PO Question Papers
Free Online Mock Test Series with Solutions
Previous Year Question Papers PDF with Solutions

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?

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?

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

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?

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?

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:

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

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Problems on Trains – Concept, Formulas and Practice Questions

Problems on trains: concept.

Problems on Trains, like concepts of speed, distance, and time, focus on evaluating a train’s speed, distance traveled, and time spent under various conditions.

The weightage of questions asked from this topic in the quantitative aptitude component of various government exams frequently ranges between 1 or 2 marks, and the most common exams that contain this topic in its syllabus include Bank, Insurance, SSC, RRB, and other important government exams.

Important formulas

formulas
The train’s speed is calculated as	$$ \frac{the \ total \ distance \ reached}{divided \ by \ the \ time \ taken} $$
If the length of two trains is specified, say a and b, and the trains are moving in opposite directions with speeds of x and y, then the time taken for trains to cross each other	$$\frac{(a+b)}{(x+y)}$$
If the length of two trains is specified, say a and b, and they are moving in the same direction, with speeds x and y consequently, the time taken to cross each other is	$$\frac{(a+b)}{(x-y)}$$
When the starting time of two trains is the same from x and y towards each other, and after crossing each other, they needed t and t time to reach y and x respectively, then the ratio between the speed of two trains	$$ √t2: √t1 $$
If two trains leave x and y stations at times t and t , respectively, and travel at speeds L and M, then the distance from x where two trains meet is	$$ = (t2 – t1) × \frac {product \ of \ speed}{difference\ in \ speed} $$
If a train’s average speed without a stoppage is x and it covers the same distance with a stoppage at an average speed of y, then the rest time per hour	$$ = \frac {difference\ in \ average\ speed}{speed \ without \ stoppage}$$
If two trains of equal lengths and different speeds take t and t time to pass a pole, then the time taken for them to cross each other if they are running in opposing directions	$$ = \frac{2×t1×t2}{t2+t1}$$
If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken for them to cross each other if they are heading in the same direction	$$ =\frac{2×t1×t2}{t2-t1} $$

Tips & Tricks for Solving Train Problems

To help hopefuls prepare for and conquer the quantitative aptitude section, here are a few pointers that will help you solve train problems faster and more efficiently:

Always read the question carefully and do not hasten to answer it, as train-based questions are frequently given in a complex manner.
After reading the questions, try to apply a formula to them; this may result in a direct solution and save you time.
Don’t guess if you’re not sure. Since there is negative marking in competitive exams, make sure you don’t make assumptions and answer the questions.
If you are unable to answer, do not overcomplicate the question or devote too much effort to solving it.
In case of confusion, you can also refer to the options supplied in the objective type papers and try to discover the answer using the options given.

Practice Quizzes

– Coming Soon

Sample Questions: Problems on Trains

Q1. A train takes 90 seconds to cross a poll with speed of 60 km/h. Find the length of the train?

a) 1500 m b) 1250 m c) 1350 m d) 1400 m

Answer: (A) Speed of train = 60 km/h × 5/18 × 90 =1500m

Q2. A train crosses a pole in 15 sec and a 100 m long platform in 25 sec, what is the length of the train?

a) 90 m b) 120 m c) 150 m d) 180 m

Answer: C Let the speed of train be x m/s Length of the train = 15×x = 15x Train crosses 100 m long platform in 25 sec Total length which the train is covering (15x + 100) m Time taken = 25 sec 15x + 100 = 25 × x 100 = 10x 10 m/s = x Length of the train = 10 × 15 = 150 m

Q3. How many poles a train crosses when travelling with a speed of 45 kmph in 4 hour. If the distance between two poles is 50 m and poles are counting from starting.

a) 1001 b) 3601 c) 3000 d) 1801

Answer: B Distance = Speed × Time = 180 × 1000 = 180000 No. of poles = 180000/50 = 3600

Q4. A train travel with a speed of 7 kmph and another train travel with a speed of 14 kmph. If they cross each other then find the average speed.

a) 17/3 kmph b) 28/3 kmph c) 29/3 kmph d) 19/3 kmph

Answer: B Average Speed = (2 × 7 × 14)/ (7 + 14) = 196/21 = 28/3 kmph

Q5. A train starts from station A at the speed of 50 km/hr and another train starts from station B after 30 min at the speed of 150 km/hr towards each other. Find the distance of their meeting point from Station A. The distance between A and B is 725 km.

a) 200 km b) 250 km c) 225 km d) None of these

Answer: A Distance travelled by first train in ½ hour = 50 × ½ = 25 km Remaining distance = 725 – 25 = 700 Time = 700/(150+50) = 3.5 hour Relative speed = 150 + 50 = 200 kmph Distance travelled by first train in (3.5+0.5) hour = 50 × 4 = 200 km

Q6. Train A of length 250 m crosses a pole in 25 seconds. Train B travelling at the same speed crosses a 400 m long platform in 1 minute. Find the time taken by train B to cross train A, if the train A is stationary.

a) 45 seconds b) 42 seconds c) 40 seconds d) 48 seconds

Answer: A Speed of train A = 250/25 = 10 m/sec So, speed of train B = 10 m/sec Let the le o B ‘x’ . Then, (x + 400)/10 = 60 x = 200 m Total length of both trains = (250 + 200) = 450 m So, time taken by train B to cross train A = 450/10 = 45 seconds.

Q7. At starting 1/3rd of passenger left and 96 passengers boarding the train, again 1/2 of passenger left and 12 passengers boarding the train now there are total 248 passengers are in the train. Find how many passengers are there at starting?

a) 865 b) 664 c) 564 d) 789

Answer: C According to the question, 248 – 12 = 236 1/2 of passenger left the train it means passenger = 2 ×236 = 472 If 96 passengers already board the train then = 472 – 96 =376 1/3 rd of passenger left the train it means 2/3x = 376 x = 188 × 3 = 564 So, initially there are total 564 passengers.

Q8. The Length of train A is 200 m and length of train B is 400 m. They travel in same direction they will take 30 sec and they travel in opposite direction they will take 6 sec to reach the destination. Find the total speed of the train.

a) 6000 km/hr b) 3000 km/hr c) 7200 km/hr d) 3600 km/hr

Answer: D Speed = Distance/time (s1 + s2)/ (s1 – s2) = 5/1 s1/ s2 = 3/2 When train travel in opposite direction, 600 = 5x × 6 600 = 30x x = 600/30 x = 20 Total speed = 5x = 5 × 20 = 100 m/sec = 1000 × 18/5 = 3600 km/hr

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Frequently Asked Questions About Problems on Trains

Q1. What is the definition of a train problem? Problems on Trains: Concept, Tips, Tricks, and Examples Train Problems – A Basic Concept. Train problems, like the notion of speed, distance, and time, are centered on evaluating a train’s speed, distance traveled, and time spent under various conditions.

Q2. What is the formula for speed and time train problems? The formula t = d/s indicates that time equals distance divided by speed, which ultimately yields the time measured in train problems. Ans. To find the speed in train problems, use the formula speed = distance divided by time.

Q3. What is the most important formula for a train? Remember some important formulas for train problems to get quick solutions. x km/hr = x*(5/18) m/s, but x m/s equals x*(18/5) km/hr. The time it takes for a train of length/meters to pass a pole, a single post, or a standing man is equivalent to the time it takes to cover/meters.

Train Problems, Check Example, Formulas, Shortcuts

Train Problems

Problems on train are a common topic in competitive exams, particularly in tests related to quantitative aptitude and reasoning. These problems are designed to test the candidate’s ability to solve numerical problems related to train travel, such as distance, speed, time, and acceleration. In this article, we will explore some common types of problems on train that are likely to appear in competitive exams and how to solve them.

Train Problems Example

Distance and Speed Problems One of the most common types of problems on train that appear in competitive exams involves calculating the distance, speed, or time taken by a train to travel a certain distance. For example, a question may ask how long it takes for a train traveling at a speed of 60 km/hr to cover a distance of 240 km. To solve this problem, we can use the formula:

Time taken = Distance / Speed

In this case, the time taken would be:

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Time taken = 240 km / 60 km/hr = 4 hours

Another variation of this type of problem involves two trains traveling towards each other on the same track, starting from different points. In this case, we can use the formula:

Time taken = Total Distance / Total Speed

For example, if two trains are traveling towards each other at speeds of 50 km/hr and 60 km/hr respectively and the distance between them is 300 km, we can calculate the time taken for them to meet as follows:

Total speed = 50 km/hr + 60 km/hr = 110 km/hr Time taken = 300 km / 110 km/hr = 2.73 hours

Time and Rate Problems Another common type of problem on train that appears in competitive exams involves calculating the speed or rate of the train based on the time taken to cover a certain distance. For example, a question may ask what the speed of a train is if it takes 2 hours to cover a distance of 120 km. To solve this problem, we can use the formula:

Speed = Distance / Time

In this case, the speed would be:

Speed = 120 km / 2 hours = 60 km/hr

Another variation of this type of problem involves calculating the distance covered by the train based on the time taken to travel at a certain speed. In this case, we can use the same formula as before:

Distance = Speed * Time

For example, if a train is traveling at a speed of 80 km/hr and it takes 3 hours to reach its destination, we can calculate the distance covered as follows:

Distance = 80 km/hr * 3 hours = 240 km

Average Speed Problems Calculating the average speed of a train over a certain distance is another common type of problem on train that appears in competitive exams. For example, a question may ask what the average speed of a train is if it travels a distance of 400 km in 8 hours. To solve this problem, we can use the formula:

Average speed = Total distance / Total time taken

In this case, the average speed would be:

Average speed = 400 km / 8 hours = 50 km/hr

Another variation of this type of problem involves finding the average speed of the train over two different distances. For example, if a train travels at a speed of 60 km/hr for the first half of its journey and at a speed of 80 km/hr for the second half, we can calculate the average speed as follows:

Total distance = Distance for the first half + Distance for the second half = 0.5D + 0.5D = D

Total time taken = Time taken for the first half + Time taken for the second half

Time taken for the first half = Distance / Speed = 0.5D / 60 km/hr = D / 120 km/hr Time taken for the second half = Distance / Speed = 0.5D / 80 km/hr = D / 160 km/hr

Total time taken = D / 120 km/hr + D / 160 km/hr = 2D / (3/2 + 4/5) km/hr = 720D / 29 km/hr

Average speed = Total distance / Total time taken = 2D / (720D / 29) km/hr = 58.125 km/hr

Relative Speed Problems Relative speed problems on train involve calculating the speed or distance between two trains traveling in opposite directions or the same direction. For example, a question may ask what the relative speed of two trains is if one is traveling at 50 km/hr and the other is traveling at 60 km/hr in the opposite direction. To solve this problem, we can simply add the speeds of both trains:

Relative speed = Speed of train 1 + Speed of train 2

In this case, the relative speed would be:

Relative speed = 50 km/hr + 60 km/hr = 110 km/hr

Another variation of this type of problem involves calculating the distance between two trains if they are traveling towards each other. For example, if two trains are traveling towards each other at speeds of 40 km/hr and 60 km/hr respectively and the distance between them is 200 km, we can calculate the time taken for them to meet as follows:

Relative speed = Speed of train 1 + Speed of train 2 = 40 km/hr + 60 km/hr = 100 km/hr Time taken = Distance / Relative speed = 200 km / 100 km/hr = 2 hours

Acceleration Problems Acceleration problems on train involve calculating the time taken by a train to reach a certain speed or distance. For example, a question may ask how long it takes for a train to reach a speed of 100 km/hr if it accelerates at a rate of 10 km/hr^2. To solve this problem, we can use the formula:

Time taken = (Final speed – Initial speed) / Acceleration

Time taken = (100 km/hr – 0 km/hr) / 10 km/hr^2 = 10 hours

Another variation of this type of problem involves calculating the distance covered by the train in a certain time, given its initial speed and acceleration rate. In this case, we can use the formula:

Distance = Initial speed * Time + 0.5 * Acceleration * Time^2

For example, if a train is traveling at a speed of 20 km/hr and accelerates at a rate of 5 km/hr^2 for 2 hours, we can calculate the distance covered as follows:

Distance = 20 km/hr * 2 hours + 0.5 * 5 km/hr^2 * (2 hours)^2 = 50 km

Train Problems for SSC CHSL – Download Free E-book

Sneak peak of train problems for ssc chsl e-book.

Train Problems for SSC CHSL

1. Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/h f and 36 km/h. The faster train passes the slower J train in 36 s. The length of each train is

2. A train 300 m long is running with a speed of 54 km/h. In what time will it cross a telephone pole?

3. Two trains of length 180 meters with velocity 30 m/s and 60 m/s travel in opposite directions and if the initial distance between them is 0.54 kilometers then what is the time taken for their tails to cross each other?

4. A train moves at a speed of 108 kmph. Its speed in meters per second is:

C) 18

5. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

A) 79.2 km/hr

B) 79 km/hr

C) 70 km/hr

D) 69.5 km/hr

6. A train travels a distance of 480 km at uniform speed. Due to breakdown, its speed is reduced by 10 km/hr and hence it travels the destination 8 hours late. Find the initial speed of the train.

A) 20 km/hr

B) 35 km/hr

C) 25 km/hr

D) 30 km/hr

7. A train travelling with constant speed crosses a 96 m long platform in 12 sec and another 141 m long platform in 15 sec. The length of the train and its speed are

A) 84 m, 54 km/h

B) 84 m, 60 km/h

C) 64 m, 54 km/h

D) 64 m, 44 km/h

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SSC CGL Syllabus 2024 and Exam Pattern

Train Problems Formula

The formula for calculating train problems can vary depending on the specific context and type of problem being addressed. However, some common formulas that may be used include:

Distance = Speed x Time: This formula is commonly used to calculate the distance that a train can travel based on its speed and the time it takes to complete the journey.
Acceleration = Change in Velocity / Time Taken: This formula is used to calculate the rate at which a train can accelerate or decelerate, based on the change in its velocity over a given time period.
Braking Distance = (Initial Speed ^ 2 – Final Speed ^ 2) / (2 x Deceleration): This formula is used to calculate the distance that a train will need to come to a complete stop, based on its initial speed, final speed, and the rate at which it can decelerate.
Power = Force x Velocity: This formula is used to calculate the amount of power required to move a train at a given velocity, based on the force required to overcome resistance and maintain motion.
Train Capacity = Number of Cars x Passenger Capacity per Car: This formula is used to calculate the maximum number of passengers that a train can carry, based on the number of cars it has and the passenger capacity per car.

Train Problems Shortcuts

Here are some shortcuts that can be useful in solving train problems quickly:

If two trains are moving in the same direction, the relative speed between them is the difference between their speeds. Example: If train A is moving at 60 km/hr and train B is moving at 40 km/hr in the same direction, their relative speed is 60 – 40 = 20 km/hr.
If two trains are moving in opposite directions, the relative speed between them is the sum of their speeds. Example: If train A is moving at 50 km/hr and train B is moving at 70 km/hr in opposite directions, their relative speed is 50 + 70 = 120 km/hr.
The time taken by a train to pass a stationary object (such as a pole or a platform) is equal to the length of the train divided by its speed. Example: If a train of length 150 meters passes a pole in 15 seconds, its speed is (150/15) m/s = 10 m/s or 36 km/hr.
The time taken by two trains to cross each other is equal to the sum of their lengths divided by the sum of their speeds. Example: If two trains of lengths 200 meters and 250 meters respectively cross each other in 20 seconds, their speeds are (200+250)/20 m/s = 22.5 m/s or 81 km/hr.

By using these shortcuts, one can quickly solve train problems without having to write down and solve long equations.

Train Problems – Conclusion

In conclusion, problems on train are a common topic in competitive exams, particularly in tests related to quantitative aptitude and reasoning. By understanding the formulas and techniques used to solve these problems, candidates can increase their chances of success in these exams.

Ans. The formula for calculating train problems can vary depending on the specific context and type of problem being addressed. for more information read the full article.

Ans. No, you can’t download pdf but you can bookmark this page for future use case.

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Problems on Trains: Definition, Rules, Solved Examples, Formulas

Questions on speed, time, and distance are common in quantitative aptitude section of most government job exams and bank exams. Among these, problems on trains , particularly concerning the speed of train, the distance traveled by the train, and the time taken by the train to traverse a particular distance are quite popular. Other common types of questions asked include ones when two trains are moving in the same direction or in opposite directions. The problems on trains must be considered as a special case because trains are considerably long structures. We solve these problems using the concept of linear equations in two variables. Let us discuss the problems related to trains and their formulas one by one.

Introduction to Speed, Time, Distance Formula

Speed is defined as the time taken by an object to cover a unit distance (1 meter or 1 kilometre). It can be measured as the ratio of the distance travelled by a body in a given period.

The SI unit of speed is $\rm{meter/second}$; however, the commonly used unit of speed in daliy life is $\rm{kilometre/hour}$.

$ {\text{Speed=}}\frac{ { {\text{Distance}}}}{ { {\text{Time}}}}$

To calculate the distance covered by the object or the time taken to cover the distance, we can use the speed formula by substituting the values of the known quantities in it.

$ {\text{Distance=Speed} \times \text{Time}}$

$ {\text{Time=}}\frac{ { {\text{Distance}}}}{ { {\text{Speed}}}}$

We will use the same concept to solve the problems on trains. We also calculate the relative speed of two trains moving in the opposite direction and same direction.

Application of Equations in Problem on Trains

Consider two trains moving in the same or opposite direction. To find the distance travelled by the trains and the time is taken, we need to know the relative speed. In these types of problems, there will be some known and unknown quantities. To determine the unknown quantity such as time, distance and speed, we need to form an equation. Solving the equation, we can get the value of an unknown quantity.

Formulas for Problem on Trains

We know that,

$ {\text{Speed of the train}} = \frac{ { {\text{Total distance covered by the train}}}}{ { {\text{Time taken}}}}$

Before we talk about the formulas of problems on trains, some related terms are needed to discuss.

We can convert a $\rm{kilometre/hour}$ to a $\rm{meter/second}$ by multiplying it with $\frac{5}{ {18}}.$

We know that $1\,\rm{kilometer} = 1000\,\rm{meter}$ and $1\,\rm{hour} = 60 × 60 = 3600\,\rm{second}$

Now, $\frac{ {1\,{\text{kilometre}}}}{ {1\,{\text{hour}}}} = \frac{ {1000\,{\text{metre}}}}{ {3600\,{\text{second}}}} = \frac{5}{ {18}}\,{\text{metre/second}}$

The Relative Speed of Two Trains moving in the Same Direction

The relative speed will be the difference between their speed if two trains move in the same direction.

The Relative Speed of Two Trains moving in the Opposite Direction

The relative speed will be the sum of their speed if two trains move in the opposite direction.

Distance Travelled when Two Trains are moving in the Same Direction/Opposite Direction

For both cases, the trains will cover the distance that is equal to the sum of the lengths of two trains.

Distance Travelled when a Train crosses a Stationary Object

When a train crosses a stationary object such as a pole, a standing person, it will cover the distance that is equal to its length.

Distance Travelled when a Train crosses a Platform/a Bridge

When a train crosses a platform or a bridge, it will cover the distance that is equal to the sum of the length of the train and bridge or platform.

Formula of Time when $2$ Trains moving in the Opposite Direction

If the two trains are moving in opposite directions with a speed of $x$ and $y$ and the length of two trains are, $a$ and $b$ respectively.

Then, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x + y}}$

The Formula of Time when the Two Trains moving in the Opposite Direction

Note: As the trains are running in the opposite direction, the relative speed is $x + y$.

Formula of Time when $2$ Trains moving in the Same Direction

If the two trains are moving in the same direction with a speed of $x$ and $y$ and the length of two trains are $a$ and $b$ respectively.

Then, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x – y}}$

Note: As the trains are running in the opposite direction, the relative speed is $x – y$.

Formula of Time When a Train Crosses a Pole

If a train of length $a$ moving with a speed $x$, crosses a pole or a person, then the time taken to cross the pole $ = \frac{a}{x}$

Formula of Time When a Train Crosses a Bridge or a Platform

If a train of length $a$ moving with a speed $x$, crosses a platform/bridge of length $b$ then the time taken to cross the platform/bridge $ = \frac{a + b}{x}$

Solved Example Probelms on Problem on Trains

Q.1. A train running at the speed of $36\,\rm{km/hr}$ crosses a stationary object in . Find the length of the train. Ans: Given, speed of the train is $36\,\rm{km/hr}$. We know that when a train crosses a stationary, it covers the distance equal to its length. Now, $\rm{Distance = Speed} \times \rm{Time}$ Therefore, the length of the train $ = \frac{ {36 \times 10}}{ {60 \times 60}} = 0.1\, {\text{km}} = 0.1 \times 1000\, {\text{m}} = 100\, {\text{m}}$

Q.2. A train moving at $90\,\rm{kmph}$ crosses another train moving in the same direction at $180\,\rm{kmph}$ in $30\,\rm{seconds}$. Find the sum of the lengths of both the trains. Ans: Speed of train $A = 90\, {\text{kmph}} = 90 \times \frac{ {1000}}{ {3600}} = 90 \times \frac{5}{ {18}} = 25\, {\text{m}}/ {\text{sec}}$ Speed of train $B = 180\, {\text{kmph}} = 180 \times \frac{5}{{18}} = 50\, {\text{m}}/ {\text{sec}}$ The relative speed will be the difference between their speed if two trains move in the same direction The relative speed $ =( 50-25)\,\rm{m/sec} = 25\,\rm{m/sec}$ The time taken by train $A$ to cross the train $B = 30\,\rm{secs}$ When the trains are moving in the same direction, the trains will cover the distance that is equal to the sum of the lengths of two trains. $\rm{Distance = the}\,\rm{sum}\,\rm{of}\,\rm{the}\,\rm{length}\,\rm{of}\,\rm{two}\,\rm{trains} = \rm{Speed} \times \rm{Time} = 25 × 30\,\rm{m}= 750\,\rm{m}$ Hence, the sum of the lengths of both the trains is $750\,\rm{m}$.

Q.3. Two trains of equal length are running on parallel lines in the same direction at $40\,\rm{km/hr}$ and $30\,\rm{km/hr}$. The faster train passes, the slower train in $36\,\rm{seconds}$. Find the length of each train. Ans: Let us say the length of the trains is $x\,\rm{m}$, and the distance covered by it is $(x + x) = 2x\,\rm{m}$ The relative speed of the trains $ = (40 – 30)\, {\text{kmph}} = 10\, {\text{kmph}} = 10 \times \frac{5}{ {18}} = \frac{ {25}}{9}\, {\text{m}}/ {\text{sec}}$ Speed of the faster train$ = \frac{2x}{36}$ So, $ \frac{2x}{36} = \frac{25}{9} $ or, $ x = \frac{25 \times 36}{18} = 50\,\rm{m}$ Hence, the length of each train is $50\,\rm{m}$.

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Q.4. It takes $12\,\rm{seconds}$ for a $360\,\rm{m}$ long train to pass a pole. How long will it take to pass a platform of $540\,\rm{m}$ long? Ans: We know that, Speed of the train $= \frac{ { {\text{Total distance covered by the train}}}}{ { {\text{Time taken}}}}$ Speed of the train $=\frac{ {360}}{ {12}}\,\rm{m/sec} = 30\,\rm{m/sec}$ When a train crosses a platform, it will cover the distance that is equal to the sum of the length of the train and the platform. The time taken to pass a platform is $ = \frac{ {360 + 540}}{ {30}} = \frac{ {900}}{ {30}} = 30 {\text{}}\, {\text{seconds}}$

Q.5. A train $350\,\rm{m}$ long is running at a speed of $54\,\rm{km/hr}$. In how much time will it pass a bridge $100\,\rm{m}$ long? Ans: Speed of the train $ = 54\, {\text{km}}/ {\text{hr}} = 54 \times \frac{5}{ {18}} = 15\, {\text{m}}/ {\text{sec}}$ The total distance that needs to be covered by the train $= (350 + 100)\,\rm{m} = 450\,\rm{m}$ $ {\text{Time=}}\frac{ { {\text{Distance}}}}{ { {\text{Speed}}}}$ Hence,the time is taken by the train to pass the bridge $ = \frac{ {450}}{ {15}} = 30\, {\text{seconds}}$

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In this article, we have covered how to solve the problems on trains when two trains move in opposite direction/ same direction when a train crosses a stationary object/bridge/platform, the relative speed of two trains, and the relative speed of two trains.

Frequently Asked Questions (FAQ) – Problem on Trains

The frequently asked questions about problems on trains are answered here:

For solving the problems related to trains, it is essential to know the relative speed of two trains. If two trains move in the same direction, then the relative speed will be the difference between their speed. If two trains move in the opposite direction, then the relative speed will be the sum of their speed.
For both cases, the trains will cover the distance equal to the sum of the lengths of two trains.

If the two trains run in opposite directions with a speed of $x$ and $y$ and the length of two trains are $a$ and $b$ respectively.
So, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x + y}}$
If the two trains run in the same direction with a speed of $x$ and $y$ and the length of two trains are, $a$ and $b$ respectively.
So, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x – y}}$
If a train of length $a$ moving with a speed $x$, crosses a pole or a person then the time is taken to cross the pole $ = \frac{{a}}{{x}}$
If a train of length $a$ moving with a speed $x$, crosses a platform/bridge of length $b$ then the time is taken to cross the platform/bridge $ = \frac{{a + b}}{{x}}$

The problems on trains are similar to the speed, time, and distance problems. If we know the relative speed of the trains and the length of the trains, we can easily find out the time taken to cover the distance and vice versa.

We can convert $1\,\rm{km/hr}$ into $\rm{m/sec}$ by multiplying it by $ = \frac{{5}}{{18}}.$

If the distance covered by the train and the time taken to cover the distance is known, we can find the train’s speed as
${\text{Speed of the train}} = \frac{{{\text{Total distance covered by the train}}}}{{{\text{Time taken}}}}$

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GMAT Problems on Trains

Updated on
Nov 17, 2022

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.

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.

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).

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.

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Problems on Trains

25 April 2024

Quantitative aptitude questions on trains are a special case of time and distance problems. In this article, you will learn the concepts related to an important topic in Time, Speed and Distance i.e. Trains.

Formula's For Problems On Trains

1. time taken by a train of length x meters to pass a pole or standing man or a signal post is = the time taken by the train to cover x meters. .

2. Time taken by a train of length X meters to pass a stationary object of length b meters is = the time taken by the train to cover (X+ b) meters.

3. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.

4. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.

5. If two trains of length a meters and b meters are moving in opposite directions at um/s and v m/s, then:

The time taken by the trains to cross each other = (a + b) / (u + v) sec

6. If two trains of length a meters and b meters are moving in the same direction at um/ s and v m/s, then:

The time taken by the faster train to cross the slower train = (a + b) / (u - v) sec

7. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

(A's speed) : (B's speed) = (√ b: √a )

Problems On Trains

Q1) A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

A) 200 metres

B) 160 metres

C) 190 metres

D) 120 metres

Q2) A train, 130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is

A) 235 metres

B) 245 metres

C) 270 metres

D) 220 metres

Q3) A train has a length of 150 metres. It is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.

A) 152 km/hr

B) 169 km/hr

C) 182 km/hr

D) 180 km/hr

Q4) A train having a length of 240 metre passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 metre?

A) 99 seconds

B) 89 seconds

C) 120 seconds

D) 80 seconds

Q5) Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

A) 1 : 3

B) 3 : 2

C) 3 : 4

D) None of these

Q6) Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

B) 72 m

Q7) A train travelling at 60 kmph crosses another train travelling in the same direction at 50 kmph in 30 seconds. What is the combined length of both the trains?

A) 250/3 metres

B) 250/7 metres

C) 255/3 metres

Q8) Two trains start at the same time from Pune and Delhi and proceed towards each other at 80 kmph and 95 kmph respectively. When they meet, it is found that one train has travelled 180 km more than the other. Find the distance between Delhi and Pune.

A) 1200 kms

B) 2120 kms

C) 2000 kms

D) 2100 kms

Q9) Indrayani Express leaves Pune for Bombay at 17:30 hrs and reaches Bombay at 21:30 hrs. While, Shatabdi, which leaves Bombay at 17:00 hrs reaches Pune at 20:30 hrs. At what time do they pass each other?

A) 19:06 hrs

B) 18:00 hrs

C) 19:16 hrs

Q10) A train of length 240 meters crosses a pole in 12 seconds. In what time it will cross a platform of length 400 meters?

A) 33 seconds

B) 35 seconds

C) 37 seconds

D) 39 seconds

Any Questions? Look Here.

Trains going in a different direction.

Q. There are two trains of 89 m and 111 m in length running in different directions. One of this train is running at a rate of 30 km/hr and the other is 42 km/hr. Find the time these trains will clear each other.

Here it is given that the two trains are going in a different direction. So, their relative speeds will be added. Thus, the total speed is 42 + 30 = 72 km/hr or 20 m/s in metres. So, the total time required here is, the total length of the trains/relative speed = 89 +111/20 = 10 seconds.

Solve Problems related to Race here

Train crossing a platform

Q. A 120 m train is running at a rate of 54 km/hr. This train takes 102 seconds to cross the platform. Find the time it takes to cross the platform.

Here, while crossing a platform, the train will have to travel its own length in addition to the length of the bridge. First, we will convert km/hr into m/s. So, 54 km/hr = 54 x 5/18 = 15 m/s. So, the time required is 222/15 = 14.8 seconds. This is our required answer.

Trains going through a standing pole

Q. Suppose a train which is 220 meters in length is going at 60 km/hr rate. Find the time it will take to pass a man who is walking in the opposite direction at 6 km/hr.

In this question, the length of the man will be considered as 0. So, it will be solved in the same way as above. Thus, the speed of both will be added. Thus, the relative speed is 60 + 6 = 66 km/hr = 55/3 m/s.

So, the required time by the train will be, 220/55 x 3 = 12 seconds.

Practice Questions on Problems on Trains

Q. There are two trains that are running in the opposite direction. Each train has a length of 120 meters. They cross each other in 12 seconds, find the speed of the train.

A. 42 km/hr B. 48 km/hr C. 36 km/hr D. 54 km/hr

Answer: C. 36 km/hr

Q. There is a which a train running at 60 km/hr crosses in 9 seconds. What is the length of this running train?

A. 130 meters B. 140 meters C. 150 meters D. 160 meters

Answer: 150 meters

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Important Problems

Stocks and Shares
Race and Games of Skill

One response to “Race and Games of Skill”

Answer to the practice question 1 should be 28m not 32m. Please check and verify. B can travel 224m in 32 sec, but in their race A travels same in 28 sec so the race finishes at 28 sec. Distance covered by B in 28s = 224/32 * 28 = 196m. Difference between 224 and 196 is 28m.

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Time, Speed and Distance: Problems on Trains

Important Points

When two trains are going in the same direction, then their relative speed is the difference between the two speeds.
When two trains are moving in the opposite direction, then their relative speed is the sum of the two speeds.
When a train crosses a stationary man/ pole/ lamp post/ sign post- in all these cases, the object which the train crosses is stationary and the distance travelled is the length of the train.
When it crosses a platform/ bridge- in these cases, the object which the train crosses is stationary and the distance travelled is the length of the train and the length of the object.
When two trains are moving in same direction, then their speed will be subtracted.
When two trains are moving in opposite directions, then their speed will be added.
In both the above cases, the total distance is the sum of the length of both the trains.
When a train crosses a car/ bicycle/ a mobile man- in these cases, the relative speed between the train and the object is taken depending upon the direction of the movement of the other object relative to the train- and the distance travelled is the length of the train.

Solved Questions

Time, Speed and Distance: Basic concepts
Time, Speed and Distance- Basics
Time, Speed, Distance: Circular Motion
Time, Speed and Distance- Ratio Concept
Relative Speed & Problems on Trains

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Quantitative Aptitude
Problems On Trains

Problems on Trains

Problems on Trains, like the concept of speed, distance, and time, are focused primarily on analysing the speed, distance covered, and time required by a train in various situations.

Real-Life Applications of Trains Problems

Real-life examples where the concepts of Problems on Trains is involved are:

Application 1:

The relative speed notion will help us grasp the meeting sites of two things going in the same or opposing direction, such as two buses or trains heading towards each other at the same time.

Application 2:

The relative speed concept will assist us in determining the time and speed required to transport something when two objects are going in the same or opposing directions.

Trains Problems Aptitude Resources

The resources mentioned below can help you with your Trains problems aptitude preparation.

1 . Concepts

Learn important concepts related to Problems on Trains. Once you begin comprehending what has to be assessed, you develop a better understanding of the nature of the questions.

2 . Formulas

Learn important formulas linked to the Trains problems that can help you answer the questions quickly and develop a greater understanding of the concepts.

3 . Practice Problems

Practice sample problems related to the Problems on Trains topic. A candidate is more likely to comprehend the concept and improve their speed and precision the more questions they practice.

How important is the Problems on Trains topic in placement examinations?

Problems on Trains topic carry medium weightage in the Quantitative Aptitude examinations.

Is Problems on Trains difficult to learn?

No, Problems on Trains topic is not difficult to understand. Students must practice Problems on Trains on a daily basis and memorise formulas to address the problems accurately. Students must also learn different shortcuts & tricks to improve their solving speed.

What is the fastest and most effective way to learn the Problems on Trains topic?

Students must understand the foundations and formulas of Problems on Trains. They should be informed of the shortcuts and tricks for various types of questions on the topic. They must practice on a daily basis before taking a weekly mock exam.

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Problems on Trains Questions with Answers

Probs on trains quiz 5, probs on trains quiz 4, probs on trains quiz 3, probs on trains quiz 2, probs on trains quiz 1.

From the point of view of some of the major competitive exams like IBPS PO , IBPS Clerk , SBI PO , SBI Junior Associate , RRB Clerk , RRB Scale 1 Officer , SSC CGL , SSC CHSL , and LIC Assistant , problems on trains are very important. Questions from this topic are asked in different formats like finding meeting time when two trains moving in opposite direction, two trains moving in same direction, train crossing a stationary object of a given length like a platform or bridge, train crossing a stationary object like a pole or a man. A good knowledge of topics like speed, relative speed, time, distance, and formulae required to obtain them is necessary to solve these questions effectively.

Though these questions demand a good knowledge of different topics, if you practice regularly with Smartkeeda problems on trains questions with answers , you can solve train-related questions in a very short time in the exam. In our practice sets, we have included important problems on trains question with answers asked in different exams along with important techniques and short tricks required to solve these problems. You can also download practice sets of problems on trains questions pdf and learn how to use problems on trains formulae in different ways for a better score in your upcoming exams.

Frequently Asked Questions

PROBLEMS ON TRAINS WITH SOLUTIONS

1. To convert the speed km per hour to meter per speed, multiply 5/18.

2. To convert the speed meter per second to km per hour, multiply 5/18.

3. Let the length of the train be L meters.

Distance traveled to pass a standing man = L meters

Distance traveled to pass a pole = L meters

4. Let the length of the train be 'a' meters and the length of the platform be 'b' meters.

Distance traveled to pass the platform is (a + b) meters

5. If two trains are moving on the same directions with speed of 'p' m/sec and 'q' m/sec (here p > q), then their relative speed is

= (p - q) m/sec

6. If two trains are moving opposite to each other in different tracks with speeds of 'p' m/sec and 'q' m/sec, then their relative speed is

= (p + q) m/sec

7. Let 'a' and 'b' are the lengths of the two trains.

They are traveling on the same direction with the speed 'p' m/sec and 'q' m/sec (here p > q), then the time taken by the faster train to cross the slower train

= (a + b)/(p - q) seconds

8. Let 'a' and 'b' are the lengths of the two trains.

They are traveling opposite to each other in different tracks with the speed 'p' m/sec and 'q' m/sec, then the time taken by the trains to cross each other

= (a + b)/(p + q) seconds

9. Two trains leave at the same time from the stations P and Q and moving towards each other.

After crossing, they take 'p' hours and 'q' hours to reach Q and P respectively.

Then the ratio of the speeds of two t rains is √q : √p.

10. Two trains are running in the same direction/opposite direction.

The person in the faster train observes that he crosses the slower train in 'm' seconds.

Then the distance covered in 'm' seconds in the relative speed is

= length of the slower train

11. Two trains are running in the same direction/opposite direction.

The person in the slower train observes that the faster train crossed him 'm' seconds.

= length of the faster train

Problem 1 :

If the speed of a train is 20 m/sec, find the speed the train in km/hr.

speed = 20 m/sec

To convert m/sec to km/h, multiply the given m/sec by 18/5.

= 20 x 18/5 km/hr

Problem 2 :

The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform.

Distances needs to be covered to cross the platform is

= sum of the lengths of the train and platform

= 300 + 500

= 800 meters

Time taken to cross the platform is

= distance/speed

= 40 seconds

Problem 3 :

A train is running at a speed of 20 m/sec. If it crosses a pole in 30 seconds, find the length of the train in meters.

The distance covered by the train to cross the pole is

= length of the train

Given : Speed is 20 m/sec and time taken to cross the pole is 30 seconds.

distance = speed ⋅ time

length of the train = speed ⋅ time

= 20 ⋅ 30

= 600 meters

Problem 4 :

It takes 20 seconds for a train running at 54 km/h to cross a platform. And it takes 12 seconds for the same train in the same speed to cross a man walking at the rate of 6 km/h in the same direction in which the train is running. What is the length of the train and length of platform (in meters).

Relative speed of the train to man = 54 - 6 = 48 km/hr.

= 48 ⋅ 5/18 m/sec

= 40/3 m/sec

When the train passes the man, it covers the distance which is equal to its own length in the above relative speed.

Given : It takes 12 seconds for the train to cross the man So, the length of the train = relative speed x time

= (40/3) ⋅ 12

Speed of the train = 54 km/h

= 54 ⋅ 5/18 m/sec

When the train crosses the platform, it covers the distance which is equal to the sum of lengths of the train and platform

Given : The train takes 20 seconds to cross the platform.

So, the sum of lengths of train and platform

= speed of the train ⋅ time

= 300 meters

length of train + length of platform = 300

160 + length of platform = 300

length of platform = 300 - 160

= 140 meters

Hence the lengths of the train and platform are 160 m and 140 m respectively.

Problem 5 :

Two trains running at 60 km/h and 48 km/h cross each other in 15 seconds when they run in opposite direction. When they run in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. Find the length of the two trains (in meters).

When two trains are running in opposite direction,

relative speed = 60 + 48

= 108 ⋅ 5/18 m/sec

Sum of the lengths of the two trains is sum of the distances covered by the two trains in the above relative speed.

Then, sum of the lengths of two trains is

= speed ⋅ time

= 30 ⋅ 15

When two trains are running in the same direction,

relative speed = 60 - 48

= 12 ⋅ 5/18

= 10/3 m/sec

When the two trains running in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds.

The distance he covered in 36 seconds in the relative speed is equal to the length of the slower train.

length of the slower train = 36 ⋅ 10/3 = 120 m

length of the faster train = 450 - 120 = 330 m

Hence, the length of the two trains are 330 m and 120 m.

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Problems on Trains - Aptitude test, questions, shortcuts, solved example videos

Online aptitude test >> Problems on Trains - Aptitude test, questions, shortcuts, solved example videos
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1. Two trains moving in opposite direction.
2. Two trains moving in same direction.
3. A train crossing a stationary object of a given length like a platform or bridge.
4. A train crossing a stationary object like a pole or a man which can be considered as a point object.

1) If the length of one train is P and the length of second train is Q, the total distance to be covered is (P+Q)

2) Finding Relative speed:
at V m/s and V m/s, then time taken by the trains to cross each other, can be calculated by

Time Taken =	(P + Q)
	(V + V )

Time Taken =	(P + Q)
	(V – V )

Time =	L
	Speed

Time =	(L + L )
	Speed

Time =	(L + L )
	R

(P's Speed)	=	q
(Q's Speed)	=	p

km	=	1000 m	=	5	m/s
hr		60 x 60 sec		18

m	=	18	km/hr
s		5

Type 1 : I) A train crosses a stationary object on the platform. Find a) the time taken or b) length of train

Speed of train = 70 x	5	= 19.44 m/s
	18

Speed =	Distance
	Time

Time taken to cross stationary object =	250
	19.44

Speed =	10	x 60 = 40 x	5	m/sec = 11.1 m/sec
	15		18

Type 2 : I) A train of given length crosses the platform at a given speed. Find: a) Time taken to cross the platform or b) Length of platform

Speed =	(L + L )
	Time

Speed of the train = 60 x	5	= 16.66 m/s
	18

The time taken =	Distance
	Speed

=	250
	16.66

- 50 km/hr = 50 x	5	= 13.88 m/s
	18

- 7 km/hr = 7 x	5	= 1.94 m/s
	18

13.88 =	(L + L )	---- consider L as length of train and L as length of platform
	30

Type 3: Find time taken by a train to cross a person running in opposite direction at a given speed.

- 62 km/hr = 62 x	5	= 17.22 m/s
	18

- 20 km/hr = 20 x	5	= 5.55 m/s
	18

=	200	= 8.77 sec
	22.78

30 km/hr = 30 x	5	= 8.33 m/s
	18

Type 4: Find time taken by a train to cross a person running in same direction at a given speed.

- 71 km/hr = 71 x	5	= 19.72 m/s
	18

- 20 km/hr = 10 x	5	= 2.77 m/s
	18

=	180	= 10.61 sec
	16.95

55 km/hr = 55 x	5	= 15.27 m/s
	18

= Distance over speed =	300	= 19.64 sec
	16.27

Type 5: Find time taken by two trains moving in opposite direction at given speed, to cross each other

65 km/hr = 65 x	5	= 18.05 m/s
	18

80 km/hr = 80 x	5	= 22.22 m/s
	18

Time =	Distance
	Speed

Time =	450	= 11.17 sec
	40.27 sec

Time =	(P + Q)	sec
	(V + V )

10 =	(250 + 200)
	(15.27 + V )

Type 6: Two trains move at a given speed in same direction. Find: a) Time taken to cross each other b) Length of train

15 km/hr = 15 x	5	= 4.16 m/s
	18

Time =	(P + Q)	sec
	(V – V )

20 x	5	=	100	= 5.56 m/s
	18		18

Discussion Board

Problems on Trains Questions

FACTS AND FORMULAE FOR PROBLEMS ON TRAINS

1. a km/hr = [a x (5/18)] m/s.

2. a m/s = [a x (18/5)] km/hr.

3. Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.

4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + b) metres.

5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relatives speed = (u - v) m/s.

6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed = (u + v) m/s.

7. If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = ( a + b ) ( u + v ) sec.

8. If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then the time taken by the faster train to cross the slower train = a + b u - v sec.

9. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A's speed) : (B’s speed) = b : a

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is :

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.

Therefore, Man's rate against the current = (12.5 - 2.5) = 10 km/hr.

View Answer Report Error Discuss Filed Under: Problems on Trains Exam Prep: CAT Job Role: Bank PO

A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?

Relative speed =280/9 m / sec = (280/9*18/5) kmph = 112 kmph.

Speed of goods train = (112 - 50) kmph = 62 kmph.

View Answer Report Error Discuss Filed Under: Problems on Trains

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is ?

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) x (18/5)] km/hr = 45 km/hr. Let the speed of the train be 'S' km/hr. Then, relative speed = (S - 5) km/hr. S - 5 = 45 => S = 50 km/hr.

View Answer Report Error Discuss Filed Under: Problems on Trains Exam Prep: AIEEE , Bank Exams , CAT , GATE Job Role: Bank Clerk , Bank PO

Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is

Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v + v = 2v 2v = distance/time = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10 × 36/10 km/hr = 36 km/hr

A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

$train problem solving tricks$

Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was

Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = ( b : a )

Therefore, Ratio of the speeds of two trains = 9 : 4 = 3 : 2

View Answer Report Error Discuss Filed Under: Problems on Trains Exam Prep: AIEEE , Bank Exams , CAT Job Role: Bank Clerk , Bank PO

Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

Assume both trains meet after x hours after 7 am Distance covered by train starting from P in x hours = 20x km Distance covered by train starting from Q in (x-1) hours = 25(x-1) Total distance = 110 => 20x + 25(x-1) = 110 => 45x = 135 => x= 3 Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.

Time = 26 sec.

Let the length of the train be x metres.

Then,[ (x+250)/26 ]= 20

=> x + 250 = 520

=> x = 270.

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Study Material

Train Problems And Tricks with Examples

Post author: Sandeep Verma
Reading time: 4 mins read

In quantitative aptitude, Train problems are the most frequently asked questions in form of Time and Speed questions. It involves the speed, time, and distance concept, including relativity theory also.

In this article, we will get to know how to deal with train problems.

Basic Concepts

So let first see the basic concept:

Distance: When an object simply moves from one place to another. We measure it in Km or m. Time: It represents how much time an object needs to cover a particular distance. We measure it in hr or s. Speed: It simply represents at what pace an object is moving. We measure it in km/hr or m/s.

These three things relate to each other and give us a formula which is:

Speed = Distance/Time

Types of Questions Normally Asked from Train Problem

Asking questions where conversion is needed.

Converting Km/h to m/s =meter/ (minute * seconds) = 1000/(60*60) = 5/18 m/s
Converting m/s to Km/h = (minute * seconds) / meter = (60*60)/ 1000 = 18/5 Km/h

Q. A train moves with a speed of 10 km/h. What distance it will cover in 20 s?

First, convert the speed in m/s = 10 *5 /18 = 50/18 m/s

Now find the distance = d = s * t

d = (50/18)* 20 = 55.5 m

Asking Direct Question where two parameters are given and required to find the third one by simply using the distance formula

Use, Speed = Distance/time

Q. A train moves with a speed of 10 km/h. Find its distance after traveling for 2 hours?

Speed =10km/h

Distance= ?

Time = 2 hrs

10km/h = ?/2 hrs

distance = 10km/h *2 hrs

distance = 20km

Asking a question about a moving object relative to a stationary object such as a person, bridge, platform, and more

If a stationary object is a poll, person or a tree and to know when a moving object would completely cross that stationary object= length of object/ speed
If a stationary object is a bridge, platform and to know when a moving object would completely cross that stationary object= length of object + length of platform or bridge/ speed

Q. A train is 600 m long and moving with a speed of 200 m/s. What time does it cross 600 m long Platform?

Speed = 200 m/s

Distance = ( length of train + length of platform) / t

t = (600m + 600m )/200 m/s

t = 1200m/200 ms

Asking Train Problem Questions based on Relativity Theory

Time = (length of first moving object + length of a second moving object)/ (Speed of the first train – Speed of the second train)
Time = (length of first moving object + length of a second moving object)/ (Speed of the first train + Speed of the second train)

Q. Train A 200 m long moves with a speed of 150 m/s and Train B 300 m long moves with a speed of 150 m/s. If both trains are opposite to each other, at what time they cross each other.

Distance = length of train A + length of train B = 200 + 300 = 500 m

Speed = speed of train A + speed of train B = 150 + 150 = 300 m/s

t = 500/300 = 5/3 s

Age problems tricks and shortcuts with examples, statement and argument reasoning tricks with example, coding and decoding reasoning tricks with examples, leave a reply cancel reply.

Aptitude - Problems on Trains

Why should i learn to solve aptitude questions and answers section on "problems on trains".

Learn and practise solving Aptitude questions and answers section on "Problems on Trains" to enhance your skills so that you can clear interviews, competitive examinations, and various entrance tests (CAT, GATE, GRE, MAT, bank exams, railway exams, etc.) with full confidence.

Where can I get the Aptitude questions and answers section on "Problems on Trains"?

IndiaBIX provides you with numerous Aptitude questions and answers based on "Problems on Trains" along with fully solved examples and detailed explanations that will be easy to understand.

Where can I get the Aptitude section on "Problems on Trains" MCQ-type interview questions and answers (objective type, multiple choice)?

Here you can find multiple-choice Aptitude questions and answers based on "Problems on Trains" for your placement interviews and competitive exams. Objective-type and true-or-false-type questions are given too.

How do I download the Aptitude questions and answers section on "Problems on Trains" in PDF format?

You can download the Aptitude quiz questions and answers section on "Problems on Trains" as PDF files or eBooks.

How do I solve Aptitude quiz problems based on "Problems on Trains"?

You can easily solve Aptitude quiz problems based on "Problems on Trains" by practising the given exercises, including shortcuts and tricks.

Problems on Trains - Formulas
Problems on Trains - General Questions
Problems on Trains - Data Sufficiency 1
Problems on Trains - Data Sufficiency 2
Problems on Trains - Data Sufficiency 3

Speed =		60 x	5		=		50
			18				3

Length of the train = (Speed x Time).

		50	x 9
		3

Speed of the train relative to man =		125
		10

=		25
		2

=		25	x	18
		2		5

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = ( x - 5) km/hr.

Speed =		45 x	5		=		25
			18				2

Time = 30 sec.

Let the length of bridge be x metres.

Then,	130 +	=	25
	30		2

Video Explanation: https://youtu.be/M_d8WufJWKc

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x metres,

and length of the second train = 17 y metres.

	27 + 17	= 23
	+

		=	3	.
			2

Speed =		54 x	5
			18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then,	+ 300	= 15
	36

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Problems on Trains – Quantitative Aptitude

Quantitative aptitude – problems on trains.

Here we will discuss all the basic rules and formulas of “Problems on Trains” chapter. So, let’s starts the basic concepts of problems on trains.

What is Problems on Trains ?

Questions on trains are very common in every competitive exams. In this type of questions we need to find the speed of train, total distance covered by a train and few other things related to trains.

To find out the answer of this type of questions, we need to know few basic formulas of Trains. So let’s discuss those formulas here.

Basic Formulas of Problems on Trains

x km/hr = x X (5/18) m/sec
y m/sec = y X (18/5) km/hr
Speed = Distance / Time
Velocity = Displacement / Time
Time taken by a x meters long train to pass a signal pole or a standing man or anything like this is equal to the time taken by that train to travel x meters.
Time taken by a x meters long train to pass an object of y meters of length is equal to the Time taken by that train to travel (x + y) meters.
Let’s assume that two objects or two trains are moving in the same direction at S1 m/s and S2 m/s where S1 > S2 , then their relative speed would be (S1 – S2) m/s .
Let’s assume that two objects or two trains are moving in the opposite directions at S1 m/s and S2 m/s , then their relative speed would be (S1 + S2) m/s .

Suppose two trains of length x meters and y meters are moving in the opposite directions at S1 m/s and S2 m/s , then

The time taken by two trains to cross each other is = (x+y) / (S1+S2) seconds

Suppose two trains of length x meters and y meters are moving in the same directions at S1 m/s and S2 m/s where S1 > S2 , then

The time taken by the faster train to cross the slower train = (x+y) / (S1-S2) seconds

Assume that two trains or two objects start from two points A and B towards each other at the same time and after crossing they take x and y seconds to reach B and A respectively. Then, A’s speed : B’s speed = √x : √y

So, this is all basics of problems on trains chapter. Now if you have any questions regarding problems on trains, then please feel free to ask us. We will discuss your question here in www.AptitudeTricks.com . Put your question on comments section down below.

Problems on Trains Tricks and Shortcuts For Bank Exams: Download PDF

Nov 16 2023

Problems on Trains Tricks and Shortcuts For Bank Exams: Dear Aspirants, In this problems on Trains Tricks for bank exams article we have provided the problems on trains tricks pdf. If you are preparing for the upcoming bank exams and other competitive exams efficiently, you can use these problems on trains tricks. Problems on trains are one of the most significant topics in the quantitative aptitude section of the bank exams. In most of the bank exams such as sbi clerk, sbi po, ibps po, ibps clerk, rrb po, rrb clerk, and other insurance exams problems on trains play a prominent role. So you must be familiar with the problems on trains tricks to solve various types of questions simply by using the problems on trains tricks for bank exams. Problems on train tricks will help you to make your calculations easy with speed and accuracy while solving the questions in the bank exams. In many competitive exams like ssc chsl, ssc cgl, ssc mts, and railways they frequently asked about problems on trains questions frequently. We have provided the problems on trains tricks pdf for bank exams in this problems on trains shortcuts for bank exams post. These problems on trains tricks will enhance your preparation level for the future bank exams.

Practice problems on train questions - Free pdf

Problems on Trains Tricks and Shortcuts PDF For Bank Exams

Here you can collect the problems on trains tricks pdf for bank exams. If you want to increase your preparation level for the upcoming bank exams and other competitive exams you can make use of these problems on trains tricks for bank exams. This problems on trains tricks pdf will help you for further practice. Download the problems on trains tricks pdf in this problems on trains tricks for bank exams article.

Download problems on trains tricks and shortcuts pdf for bank exams

Problems on Trains Tricks and Shortcuts For Bank Exams

You can check the problems on trains tricks for bank exams here. If you are going to appear for future bank exams and other competitive exams you can exploit these problems on trains tricks. These problems on trains tricks for bank exams will help you to make your calculations easier while solving the questions in the bank exams. Here you can learn the important problems on trains tricks for bank exams and start your preparation effectively.

To find the speed of the train you can use the trick,

speed of the train = Total distance covered by the train / Time taken

Suppose two trains are moving in the same direction at u kmph and v kmph such that u>v, then their relative speed = u-v kmph.
Suppose two trains are moving in opposite directions at u kmph and v kmph. Then, their relative speed = (u+v) kmph.
The distance covered by train in passing a pole or a standing man is equal to the length of the train
If a train passes a platform, bridge, etc. has some length, then the distance covered by trains is equal to the sum of the lengths of the train and that particular object.
First of all practice on a set of problems on trains questions by using these problems on trains tricks for bank exams. It will help you to be more familiar with the problems on trains questions.
You have to be proficient with the problems on trains formula for bank exams to make your calculation easier with speed and accuracy. The problems on trains formula pdf for bank exams is attached in this problems on trains tricks for bank exams post. You can download it and start practicing for your competitive exams.

Download problems on trains formula pdf for bank exams

We hope that these problems on trains tricks and shortcuts for bank exams will be useful for your upcoming bank exams and other competitive exams. This problems on trains tricks article will help you to increase your ability to solve all the levels of trains problems. Stay connected on our Guidely team to get more details to enhance your preparation level for forthcoming government examinations.

Problems on Trains Tricks and Shortcuts for Bank Exams FAQs

Q. How to find the speed of the train?

A . To find the speed of the train you can use the trick,

speed of the train = Total distance covered by the train / Time taken

Q. What are the important problems on trains tricks and shortcuts for bank exams?

A. The important problems on trains tricks and shortcuts for bank exams are mentioned in the above article. Kindly go through the above problems on trains tricks for bank exams post to know more problems on trains shortcuts for bank exams.

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Math Wheels for Note-taking?

Teaching Problem Solving in the Middle School Classroom

If you are teaching problem solving in your middle school classroom, then you have got to check out this post! I share all of my best resources and blog posts for helping you to teach problem solving skills in your math classroom.

I love teaching problem solving to my middle schoolers! By this stage in their math journey, they’ve already laid a foundation. Now, I get to show them all the different ways they can approach a problem. It’s so rewarding to see how unique each student is, especially when one strategy works great for one and another for someone else. In the end, though, they all reach the right answer, which is what really matters. This process also sparks some amazing, authentic math conversations in the classroom. Today, I’m excited to share all the posts I’ve written to help with teaching problem solving!

Helping our students develop problem solving skills can be difficult. It takes time and lots of opportunities to practice those skills. Over the years I’ve used a variety of teaching strategies and activities when it comes to problem solving. Some worked well and some not so much. So I’ve pulled together the things that worked well to share with you here. I hope that as you read through the posts you will find some nuggets that will help you make teaching problem solving easier and more effective.

Roundup of Posts for Teaching Problem Solving

Teaching math problem solving strategies.

This post is all about helping our students develop strong problem-solving skills through a variety of strategies. I highlight different approaches that can guide our students in breaking down math problems, making them more manageable and less intimidating. It also dives into why exposing our students to multiple strategies is important. It gives them the tools to find what works best for their individual learning styles.

This image showcases a set of doodle notes resources you can use when teaching problem solving.

My Problem Solving Doodle Notes resource is a fantastic tool for teaching problem solving in a way that’s interactive and visually engaging for students. In this blog post, I share how I’ve used this resource to teach a variety of problem solving strategies that make breaking down math problems easier. The doodle notes allow my students to keep track of various strategies like guessing and checking, working backward, drawing diagrams, and making organized lists. What I love most about this resource is how it encourages students to take ownership of their learning by keeping these notes as a reference all year long. It’s a fun and effective way to reinforce different methods for teaching problem solving!

To learn more about these problem solving strategies and the doodle notes read the full article here .

How to Teach Real Life Math Problem Solving Activities

My next post is all about building strong problem-solving skills in our students using real-life math activities. My experience in the classroom has led me to the conclusion that students love math when they see its relevance. There’s nothing more relevant than real-life examples of how problem solving skills are used in the day-to-day.

In this post, I explore different strategies that help students break down complex problems. This helps to make them feel less overwhelmed and more approachable. The post also explains why it’s important to introduce a variety of methods so that our students can discover what works best for them. By providing them with options, we empower them to choose strategies that fit their learning style.

5 Ways to Practice Problem Solving in Middle School

This photo shows a group of middle school students working together.

The next post emphasizes the importance of teaching students to break down complex problems into smaller, manageable steps. This one step helps them feel more confident and less overwhelmed. I also explore how teaching problem-solving approaches, such as drawing diagrams, working backward, and using logical reasoning, gives our students the flexibility to find the best method for their unique learning style.

The post also explains why building these skills is crucial for our students’ overall math success. It acknowledges that our students will face more challenging concepts. If you’re looking for ways to make teaching problem solving engaging and effective, this post offers a range of techniques that can be easily incorporated into your lessons!

Decimal Operations Math Problem Solving

Sometimes our problem solving skills change a little when it comes to specific skills and concepts. In this post, I share tips and ideas for teaching problem solving when it comes to decimals. I focus on helping students strengthen their problem solving skills through decimal operations.

This post dives into different strategies that guide our students in working through multi-step problems involving decimals. I share how I have taught problem solving skills that make the process feel less daunting. By including a variety of methods, our students can approach decimal problems from angles that make sense to them. Some of the problem solving skills I share in this post include teaching students how to use estimation, logical reasoning, or step-by-step calculations. This post highlights the importance of practicing these skills to build confidence and accuracy when tackling decimal operations. If your students are struggling with decimals and problem solving, this post is a must read!

Help Middle School Math Students Improve Problem Solving Skills

This photo highlights a bookmark you can give students when teaching problem solving strategies.

Ready to help your students expand their repertoire of problem solving strategies? This post will help! This post dives into effective ways to help middle schoolers improve their problem-solving skills in math. It covers different approaches that can simplify the process for our students. These approaches can break problems down step by step and make them more approachable.

By introducing a variety of strategies, our students gain the tools they need to navigate more complex math problems with confidence. The post also emphasizes the importance of consistency and practice in building these skills. If you’re looking for actionable ways to support your students’ growth in math while teaching problem solving, I share some great tips in this post!

Problem Solving Math Wheels

These math wheels are a great tool to use when teaching problem solving.

If you’ve been a follower, then you probably already know how much I loved using math wheels in the classroom. They are one of my absolute favorite tools for students. In this post, I dive into how you can use the Problem Solving Math Wheel to teach a variety of problem solving strategies.

These wheels allow our students to visually break down problems step by step. They also help them organize their strategies and make connections between different methods. By rotating through various approaches, such as guess and check, working backward, or drawing diagrams, our students can see how each technique plays a role in finding the solution. It’s a fantastic way to make abstract concepts more concrete. When we do, we are giving our students the tools to confidently approach math problems. Whether you’re working on basic operations or more complex equations, math wheels are a creative resource for teaching problem-solving skills.

Using Collaboration to Improve Math Problem Solving

If there is one thing our middle school students love it is collaboration. Any time we can add opportunities for our students to work together we have increased engagement. In this post, I explore the benefits of using collaborative problem-solving in middle school math. It emphasizes how working together allows our students to tackle challenging problems by sharing different strategies and perspectives.

Collaborative problem solving boosts critical thinking and fosters communication and teamwork skills. The post highlights how this approach encourages our students to explain their reasoning, ask questions, and build on each other’s ideas. This makes math more engaging and interactive. The post offers great strategies to use while teaching problem solving to your students!

How to Teach Problem of the Week in Middle School Math

We all know the saying “An apple a day keeps the doctor away.” But what if we applied this concept to helping our students improve their problem solving skills? In this post, I highlight the effectiveness of using a Problem of the Week to build strong problem-solving skills in middle school math.

This image highlights a "Problem of the Week" resource you can use in your middle school classroom.

In this post, I dive into how implementing a Problem of the Week can boost problem-solving skills in middle school math. This approach gives our students the chance to focus on one challenging problem each week. It allows them to explore various strategies and think critically about their solutions. I outline how this method promotes deeper understanding, persistence, and encourages student discussions around their problem-solving processes. If you aim to introduce a consistent and engaging routine for teaching problem solving in your classroom, this post is a great place to start.

Metric Conversions Free Problem Solving and Matching Activity

This image highlights some free resources you can use when teaching problem solving.

Similar to the post above on teaching problem solving with decimals, this post shares the specific problem solving strategies I used when my students were learning about metric conversions. In this post, I explore an engaging approach to teaching metric conversions through a matching activity that helps solidify problem-solving skills.

In this post, I share an activity that challenges students to pair conversion problems with their correct answers. It encourages them to think critically and work through the process step by step. This method makes learning metric conversions more interactive. It also helps students build confidence in their problem-solving abilities. The post also includes a free problem-solving activity that offers extra practice for our students. This ensures they get hands-on experience with these essential math concepts.

Teaching Problem Solving Made Easier

Teaching problem solving is about giving our students the tools they need to tackle any math problem that comes their way. Whether it’s through collaborative activities, hands-on resources, or weekly challenges, there are many ways to make problem solving effective. By exposing our students to a variety of strategies, we empower them to find what works best for their unique learning styles. I hope these ideas help you to incorporate more creative problem solving techniques into your classroom!

Save for Later

Remember to save this post to your favorite math Pinterest board for quick access to these resources to help with teaching problem solving!

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Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

All subject areas in 4 th and 5 th grades
Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

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