Problems on Trains

“Train-related problems often appear in SSC, Banking, and Railway exams. They test concepts of relative speed, time, and distance.”

1. Basic Concepts and Formulas

  • Speed = Distance / Time
  • Distance = Speed × Time
  • Time = Distance / Speed
  • 1 km/h = 5/18 m/s
  • 1 m/s = 18/5 km/h
  • Relative Speed (Same Direction) = Difference of Speeds
  • Relative Speed (Opposite Direction) = Sum of Speeds
  • When train crosses a pole: Time = Train Length / Speed
  • When train crosses a platform: Time = (Train + Platform) / Speed

2. Type-Wise Questions

  • Type 1: Train crosses a pole
    Example: Length = 150 m, Speed = 30 m/s ⇒ Time = 150 / 30 = 5 sec
  • Type 2: Train crosses a platform
    Example: Train = 100 m, Platform = 50 m, Speed = 10 m/s ⇒ Time = 150 / 10 = 15 sec
  • Type 3: Two trains in same direction
    Example: 120 m and 80 m, speeds 60 km/h & 40 km/h ⇒ Relative speed = 20 km/h = 5.56 m/s ⇒ Time = 200 / 5.56 ≈ 36 sec
  • Type 4: Two trains in opposite direction
    Example: 150 m & 150 m, speeds 60 & 90 km/h ⇒ Relative speed = 150 km/h = 41.67 m/s ⇒ Time = 300 / 41.67 ≈ 7.2 sec
  • Type 5: Train passes a person walking
    Example: Train = 100 m, Speed = 40 km/h, Man = 5 km/h ⇒ Relative speed = 35 km/h = 9.72 m/s ⇒ Time = 100 / 9.72 ≈ 10.3 sec
  • Type 6: Finding train speed
    Example: 200 m train crosses pole in 20 sec ⇒ Speed = 200 / 20 = 10 m/s = 36 km/h
  • Type 7: Train passes another train completely
    Example: Lengths = 120 m and 80 m, speed = 30 and 20 m/s (same direction) ⇒ Relative = 10 m/s ⇒ Time = 200 / 10 = 20 sec
  • Type 8: Train crosses bridge
    Example: Train = 250 m, Bridge = 500 m, Speed = 18 km/h = 5 m/s ⇒ Time = 750 / 5 = 150 sec

3. Previous Year Exam Questions

  • (SSC CGL 2022): A train at 60 km/hr crosses a pole in 9 sec. Find length?
    Solution: Speed = 60 × (5/18) = 16.67 m/s ⇒ Distance = 16.67 × 9 = 150 m
  • (RRB NTPC 2020): A train 125 m long passes a man running at 5 km/h in same direction in 10 sec. Find train’s speed?
    Solution: Relative speed = 125 / 10 = 12.5 m/s ⇒ Speed = 12.5 × (18/5) + 5 = 50 km/h
  • (SSC CHSL 2019): A train 300 m long passes a platform 200 m long in 40 sec. Find speed?
    Solution: Total distance = 500 m ⇒ Speed = 500 / 40 = 12.5 m/s = 45 km/h
  • (HSSC 2021): Two trains of equal length cross a man in 6s and 8s respectively. Find the ratio of their speeds?
    Solution: Let length be L ⇒ Speed1 = L/6, Speed2 = L/8 ⇒ Ratio = 1/6 : 1/8 = 4:3

4. Tips to Remember

  • Use relative speed when train and object move in same or opposite directions.
  • Always convert km/h to m/s when using meters and seconds: 1 km/h = 5/18 m/s
  • Train crossing pole uses only its own length; platform/bridge adds extra length.
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