Trains Crossing Platforms and Poles: CAT Quantitative Aptitude
Mastering Time, Speed, and Distance (TSD) is crucial for competitive exams like the CAT. This module focuses on a common and often tricky subtopic: trains crossing poles and platforms. Understanding the fundamental concepts and applying them correctly will boost your problem-solving efficiency.
Core Concepts: Poles vs. Platforms
The key difference in problems involving trains crossing poles versus platforms lies in the 'distance' the train needs to cover. A pole is considered a point object, having negligible length. A platform, however, has a significant length.
The length of the train itself.
The length of the train plus the length of the platform.
Understanding the 'Crossing' Event
A train is considered to have 'crossed' a pole or a platform when its rear end has completely passed the pole or the end of the platform. This means the entire length of the train must traverse the relevant distance.
The time taken to cross is directly proportional to the total distance covered and inversely proportional to the speed.
The fundamental formula for TSD, Time = Distance / Speed, is applied here. For crossing a pole, Distance = Length of Train. For crossing a platform, Distance = Length of Train + Length of Platform.
Let L_t be the length of the train and S_t be its speed. Let L_p be the length of the platform.
When crossing a pole: Time = L_t / S_t When crossing a platform: Time = (L_t + L_p) / S_t
It's crucial to ensure units are consistent (e.g., meters for length, meters per second for speed, seconds for time).
Key Formulas and Unit Conversions
The most common challenge is dealing with different units. Remember these conversions:
- 1 km/hr = 5/18 m/s
- 1 m/s = 18/5 km/hr
| Scenario | Distance to Cover | Formula for Time |
|---|---|---|
| Train crossing a pole | Length of the Train (L_t) | Time = L_t / Speed |
| Train crossing a platform | Length of Train (L_t) + Length of Platform (L_p) | Time = (L_t + L_p) / Speed |
Example Scenario
A train 150 meters long is running at a speed of 72 km/hr. How long does it take to cross a pole?
Solution:
- Convert speed to m/s: 72 km/hr * (5/18) = 20 m/s.
- Distance to cover = Length of train = 150 meters.
- Time = Distance / Speed = 150 m / 20 m/s = 7.5 seconds.
Now, consider the same train crossing a platform 250 meters long. How long does it take?
Solution:
- Speed is still 20 m/s.
- Distance to cover = Length of train + Length of platform = 150 m + 250 m = 400 meters.
- Time = Distance / Speed = 400 m / 20 m/s = 20 seconds.
Always visualize the train's journey from the moment its front reaches the pole/platform to the moment its rear leaves it. This helps in correctly identifying the total distance.
Advanced Scenarios
Problems can also involve two trains crossing each other, or a train crossing a moving object (like another train or a person on a platform). These build upon the fundamental concepts of relative speed.
Trains Crossing Each Other
When two trains cross each other, the total distance to be covered is the sum of their lengths. The speed used is their relative speed. If they move in the same direction, relative speed is the difference of their speeds. If they move in opposite directions, relative speed is the sum of their speeds.
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Practice and Strategy
Consistent practice is key. Focus on setting up the problem correctly by identifying the total distance and speed. Pay close attention to unit conversions. For CAT, aim to solve these problems within 30-45 seconds.
Learning Resources
Provides a comprehensive overview of TSD concepts, including formulas and basic examples relevant to competitive exams.
Offers a collection of CAT-level questions on Time, Speed, and Distance, with detailed solutions to help understand problem-solving approaches.
A foundational resource explaining the basic principles of Time, Speed, and Distance, ideal for building a strong understanding.
Specifically addresses train-related problems within TSD, covering scenarios like crossing poles and platforms with examples.
A video tutorial explaining the core concepts of Time, Speed, and Distance, including how to approach train-related questions.
This video focuses on Time, Speed, and Distance for the CAT exam, with a good section on train problems and their solutions.
Provides a set of practice questions on Time, Speed, and Distance, allowing learners to test their understanding and application of concepts.
A discussion forum thread on PagalGuy where users share tips, doubts, and solutions for train problems in quantitative aptitude.
A concise list of essential formulas for Time, Speed, and Distance, including those relevant to train problems.
Explains the fundamental concepts of Time, Speed, and Distance, with a dedicated section on train problems and their solutions.