How to Solve: Problems on Trains

How to Solve: Problems on Trains

Complete Guide for SSC / Bank / Railway Exams

Introduction

"Mastering ‘Problems on Trains’ can get you 3-5 marks in SSC CGL, Bank PO, or Railway exams—enough to push you from Tier-2 to Tier-1 or from rejection to selection. These questions test your ability to handle speed, distance, and time in real-world scenarios like overtaking, crossing platforms, or two trains moving in opposite directions. Let’s break it down so you never lose a mark again."

What You Need To Know First

Before diving in, ensure you understand: 1. Speed, Distance, Time (SDT) Basics – The formula: Distance = Speed × Time. 2. Relative Speed – How speeds add/subtract when two objects move toward/away from each other. 3. Unit Conversion – Converting km/h to m/s (multiply by 5/18) and vice versa (multiply by 18/5).

Key Vocabulary

Formulas To Know

Step-by-Step Method

Step 1: Read the Problem Carefully

• Identify what is moving (train, platform, pole, another train).
• Note directions (same or opposite).
• Extract given values (lengths, speeds, times).

Step 2: Convert Units (If Needed)

• If speed is in km/h and time is in seconds, convert speed to m/s (× 5/18).
• If distance is in meters and speed in km/h, convert speed to m/s.

Step 3: Determine Relative Speed

• Same Direction (Overtaking): Relative Speed = Faster Speed - Slower Speed.
• Opposite Direction (Crossing): Relative Speed = Speed₁ + Speed₂.

Step 4: Calculate Total Distance

• Train crossing a pole/platform: Total Distance = Train Length.
• Train crossing a platform: Total Distance = Train Length + Platform Length.
• Two trains crossing each other: Total Distance = Sum of both train lengths.

Step 5: Apply the Formula

• Time = Total Distance / Relative Speed.
• Plug in the values and solve.

Step 6: Check Units & Answer

• Ensure time is in seconds if speed is in m/s.
• If the answer is in hours/minutes, convert if needed.

Worked Examples

Example 1 – Basic (Train Crossing a Pole)

Question: A 150m train is moving at 54 km/h. How long does it take to cross a pole?

Step 1: Identify what’s moving – train and pole. - Pole is stationary (speed = 0). - Train length = 150m, speed = 54 km/h.

Step 2: Convert speed to m/s. - 54 km/h × (5/18) = 15 m/s.

Step 3: Relative speed = Train speed (pole is stationary). - Relative speed = 15 m/s.

Step 4: Total distance = Train length = 150m.

Step 5: Time = Distance / Speed = 150m / 15 m/s = 10 seconds.

Answer: 10 seconds.

What we did and why: - Converted km/h to m/s because time was in seconds. - Used train length as total distance because the pole is a point (no length). - Applied Time = Distance / Speed.

Example 2 – Medium (Train Crossing a Platform)

Question: A 200m train moving at 72 km/h crosses a 300m platform. How long does it take?

Step 1: Identify what’s moving – train and platform. - Platform is stationary. - Train length = 200m, platform length = 300m, speed = 72 km/h.

Step 2: Convert speed to m/s. - 72 km/h × (5/18) = 20 m/s.

Step 3: Relative speed = Train speed (platform is stationary). - Relative speed = 20 m/s.

Step 4: Total distance = Train length + Platform length = 200m + 300m = 500m.

Step 5: Time = Distance / Speed = 500m / 20 m/s = 25 seconds.

Answer: 25 seconds.

What we did and why: - Added train length + platform length because the train must fully pass the platform. - Converted speed to m/s for consistency with meters and seconds.

Example 3 – Exam-Style (Two Trains Crossing Each Other)

Question: Two trains, 120m and 180m long, are moving toward each other at 36 km/h and 54 km/h. How long do they take to completely cross each other?

Step 1: Identify what’s moving – two trains in opposite directions. - Train A: Length = 120m, speed = 36 km/h. - Train B: Length = 180m, speed = 54 km/h.

Step 2: Convert speeds to m/s. - Train A: 36 km/h × (5/18) = 10 m/s. - Train B: 54 km/h × (5/18) = 15 m/s.

Step 3: Relative speed (opposite direction) = 10 m/s + 15 m/s = 25 m/s.

Step 4: Total distance = Sum of train lengths = 120m + 180m = 300m.

Step 5: Time = Distance / Speed = 300m / 25 m/s = 12 seconds.

Answer: 12 seconds.

What we did and why: - Added speeds because trains are moving toward each other. - Added both train lengths because both must fully pass each other. - Converted speeds to m/s for consistency.

Common Mistakes

Exam Traps

1-Minute Recap (Night Before Exam)

"Listen up—this is your last-minute crash course for ‘Problems on Trains.’

1. Convert speeds first: km/h to m/s? Multiply by 5/18. m/s to km/h? Multiply by 18/5.
2. Relative speed:
3. Same direction? Subtract speeds.
4. Opposite direction? Add speeds.
5. Total distance:
6. Train + pole? Just train length.
7. Train + platform? Train length + platform length.
8. Two trains? Sum of both lengths.
9. Time = Distance / Speed. Plug in the numbers.
10. Double-check units: Seconds? Speed must be in m/s. Minutes/hours? Speed in km/h.

That’s it. No tricks, no shortcuts—just follow the steps. You’ve got this!