Two trains run in the same direction on parallel tracks. Lucknow Mail is 120 m long at 40 km/h; Punjab Mail is 80 m long at 50 km/h. How many seconds will they take to completely cross each other (overtaking, same direction)?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
Answer
Correct Answer: 72 sec.
Explanation
Introduction / Context:For trains in the same direction, relative speed equals the difference of speeds. The distance to be covered for a complete pass is the sum of their lengths.
Given Data / Assumptions:
- Lengths: 120 m and 80 m ⇒ total = 200 m.
- Speeds: 40 km/h and 50 km/h (same direction).
Concept / Approach:Relative speed = 50 − 40 = 10 km/h. Convert to m/s, then time = distance / speed.
Step-by-Step Solution:
Relative speed = 10 km/h = 10 * 1000 / 3600 = 2.777... m/s.Time = 200 / 2.777... = 72 s.Verification / Alternative check:2.777... m/s * 72 s = 200 m, exactly the combined length.
Why Other Options Are Wrong:8/11.5/12.5 s require much larger relative speeds than 10 km/h.
Common Pitfalls:Using sum of speeds instead of difference for same-direction motion.
Final Answer:72 sec.