Train A is 100 m long and moves at 50 km/h. It crosses Train B of length 120 m coming from the opposite direction in 6 seconds. What is the speed of Train B (in km/h)?

Introduction / Context:For trains crossing in opposite directions, the relative speed is the sum of their speeds. The distance to be covered is the sum of their lengths. This lets us compute the unknown speed given total crossing time.

Given Data / Assumptions:

• L1 = 100 m at 50 km/h; L2 = 120 m at unknown speed.
• Opposite directions; crossing time = 6 s.

Concept / Approach:Relative speed (m/s) = (L1 + L2) / time. Convert Train A's speed to m/s and subtract from the relative speed to get Train B's speed in m/s, then convert to km/h.

Step-by-Step Solution:Relative speed = (100 + 120)/6 = 220/6 ≈ 36.666... m/s.Train A speed = 50 * 1000/3600 ≈ 13.888... m/s.Train B speed = 36.666... − 13.888... ≈ 22.777... m/s = 22.777... * 3.6 ≈ 82 km/h.

Verification / Alternative check:Sum of speeds in km/h ≈ 132; 132 km/h = 36.666... m/s; times 6 s = 220 m, the combined length.

Why Other Options Are Wrong:60 or 50 km/h do not yield the required relative speed; 132 km/h is the combined speed, not Train B's speed.

Common Pitfalls:Using difference of speeds (appropriate for same direction) instead of sum for opposite directions.

Final Answer:82 km/h