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

1. 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:

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

2. 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

3. 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:

Average speed = Total distance / Total time taken

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

4. 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

5. 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

In this case, the time taken would be:

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

A) 72 m

B) 80 m

C) 50 m

D) 82 m

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

A) 17 s

B) 18 s

C) 15 s

D) 20 s

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?

A) 10 s

B) 8 s

C) 7 s

D) 5 s

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

A) 38.8

B) 30

C) 18  

D) 10.8

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:

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

1. 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.
2. 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.
3. 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.
4. 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.