Problems on Trains
Crossing poles, platforms and trains
Problems on trains are a classic topic in aptitude tests that involve calculating time, speed, and distance in scenarios involving trains crossing various objects like poles, platforms, bridges, and other trains. These problems test your understanding of relative speed and distance concepts in practical situations.
Key Formulas
Key Concepts
Crossing a Stationary Object (Pole/Signal Post)
When a train crosses a stationary object like a pole or signal post, the distance covered equals the length of the train itself. The object has negligible length, so time taken = Length of train / Speed of train. This is the simplest case of train problems.
Crossing a Platform or Bridge
When a train crosses a platform or bridge, the total distance to be covered is the sum of the train's length and the platform/bridge length. The time taken = (Length of train + Length of platform) / Speed of train. This is because the train is considered to have completely crossed only when its rear end clears the far end of the platform.
Two Trains Moving in Opposite Directions
When two trains move towards each other in opposite directions, they approach each other with a relative speed equal to the sum of their individual speeds (S + S ). The total distance to cover for complete crossing is the sum of both trains' lengths. Time = (L + L ) / (S + S ).
Two Trains Moving in Same Direction
When two trains move in the same direction, the relative speed is the difference of their speeds (faster - slower). The faster train overtakes the slower one. Time to completely pass = (L + L ) / |S - S |. This scenario requires the faster train to cover both trains' lengths at the relative speed.
A Train Crossing a Moving Object/Person
When a train crosses a moving object (person walking or another vehicle), calculate relative speed based on direction. Same direction: Relative speed = Train speed - Object speed. Opposite direction: Relative speed = Train speed + Object speed. Then use Time = Train length / Relative speed.
Unit Conversion
Train problems often require converting between km/hr and m/s. To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5. Always ensure consistent units before calculating - if lengths are in meters and times in seconds, convert speeds to m/s.
Solved Examples
Problem 1:
A train 150 m long is running at 72 km/hr. How long will it take to cross a pole?
Solution:
Given:
- Length of train = 150 m
- Speed = 72 km/hr
Step 1: Convert speed to m/s
Speed in m/s = 72 x (5/18) = 20 m/s
Step 2: Time to cross a pole
Time = Length of train / Speed
Time = 150 / 20 = 7.5 seconds
Answer: 7.5 seconds
Problem 2:
A train 200 m long crosses a platform 300 m long in 25 seconds. Find the speed of the train in km/hr.
Solution:
Given:
- Length of train = 200 m
- Length of platform = 300 m
- Time taken = 25 seconds
Step 1: Calculate total distance
Total distance = Train length + Platform length = 200 + 300 = 500 m
Step 2: Calculate speed in m/s
Speed = Distance / Time = 500 / 25 = 20 m/s
Step 3: Convert to km/hr
Speed in km/hr = 20 x (18/5) = 72 km/hr
Answer: 72 km/hr
Problem 3:
Two trains of lengths 120 m and 180 m are running towards each other at 54 km/hr and 36 km/hr respectively. How long will they take to cross each other?
Solution:
Given:
- Length of first train = 120 m
- Length of second train = 180 m
- Speed of first train = 54 km/hr
- Speed of second train = 36 km/hr
Step 1: Convert speeds to m/s
S = 54 x (5/18) = 15 m/s
S = 36 x (5/18) = 10 m/s
Step 2: Calculate relative speed (opposite direction)
Relative speed = S + S = 15 + 10 = 25 m/s
Step 3: Calculate total distance
Total distance = 120 + 180 = 300 m
Step 4: Calculate time
Time = 300 / 25 = 12 seconds
Answer: 12 seconds
Problem 4:
A train 160 m long running at 72 km/hr crosses another train 240 m long running in the same direction at 54 km/hr. How long does it take to completely pass the second train?
Solution:
Given:
- Length of faster train = 160 m, Speed = 72 km/hr
- Length of slower train = 240 m, Speed = 54 km/hr
Step 1: Convert speeds to m/s
S (faster) = 72 x (5/18) = 20 m/s
S (slower) = 54 x (5/18) = 15 m/s
Step 2: Calculate relative speed (same direction)
Relative speed = S - S = 20 - 15 = 5 m/s
Step 3: Calculate total distance
Total distance = 160 + 240 = 400 m
Step 4: Calculate time
Time = 400 / 5 = 80 seconds
Answer: 80 seconds (1 minute 20 seconds)
Tips & Tricks
- Always convert speed to m/s when lengths are given in meters - multiply km/hr by 5/18.
- Remember: When crossing a pole, only the train's length matters. When crossing a platform/bridge, add both lengths.
- For two trains: Add lengths, then use relative speed based on direction (add speeds for opposite, subtract for same).
- A train 'crossing' or 'passing' another train means from the moment the fronts meet until the rears separate.
- If a problem involves a train crossing a moving person or object, calculate relative speed first, then apply the same formulas.
- Draw a simple diagram if confused - it helps visualize what distance needs to be covered.
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