Introduction
Problems on trains are a common type of question in bank exams. These problems typically involve the speed, distance, and time taken by trains to pass each other, overtake each other, or cover a specific distance. The key concepts to focus on are relative speed, time, and distance.
This cheatsheet will provide the necessary formulas, tips, and a solved example to help you quickly solve problems on trains during the exam.
Key Concepts and Formulas
1. Basic Formula of Distance, Speed, and Time:
The fundamental formula that links distance, speed, and time is:
Distance = Speed × Time
Where:
Distance is the total length of the journey.
Speed is the rate of travel.
Time is the duration of travel.
2. Relative Speed:
When two trains are moving in opposite directions, their relative speed is the sum of their individual speeds.
Relative Speed (opposite directions) = Speed of Train 1 + Speed of Train 2
When two trains are moving in the same direction, their relative speed is the difference between their individual speeds.
Relative Speed (same direction) = Speed of Train 1 – Speed of Train 2
3. Time to Pass Each Other:
When two trains pass each other, the time taken to pass is given by:
Time = (Length of Train 1 + Length of Train 2) / Relative Speed
4. Time to Overtake a Person:
If a train is overtaking a person who is stationary, the time taken to overtake the person is:
Time = Length of Train / Speed of Train
Note: The speed of the person is considered to be 0 if they are stationary.
Important Tips for Solving Problems on Trains
1. Understanding Relative Speed:
Opposite Directions: The relative speed increases when trains are moving towards each other.
Same Direction: The relative speed decreases when trains are moving in the same direction.
2. Converting Units:
Ensure that all units are consistent. For example, if speed is in km/h, convert the time into hours, and if the speed is in m/s, convert time into seconds.
3. Distance Covered by the Train:
Remember that the distance covered by the train is not just the distance the train travels but also includes its length when calculating the time to overtake or pass something (like another train or a person).
4. Length of Trains in Passing Problems:
In problems involving two trains passing each other, the total length is the sum of the lengths of both trains.
5. Focus on Speed Differences:
For overtaking problems, make sure you understand the relative speed, especially if the objects (trains, people) are moving in different directions.
Conclusion
Problems on trains often require you to focus on relative speed and use the basic formula of distance = speed × time. Key things to remember:
Adjust relative speed based on whether the trains are moving in the same or opposite directions.
Make sure the units are consistent, and if needed, convert units.
Always sum the lengths of the trains when calculating time to pass each other.
With regular practice and understanding of the concepts, you will be able to solve these problems quickly and accurately in your bank exams.
This cheatsheet should provide you with a clear and concise approach to solving problems on trains efficiently in your bank exams!
