Pole and bridge timings – find train length A train crosses a pole in 2 s and a 250 m bridge in 7 s at uniform speed. What is the length of the train?

Introduction / Context:
Two timings with two different obstacles (point and extended) allow solving for speed and length via simultaneous equations.

Given Data / Assumptions:

• t_pole = 2 s (distance = L).
• t_bridge = 7 s (distance = L + 250 m).
• Uniform speed v.

Concept / Approach:
From pole: L = v * 2. From bridge: L + 250 = v * 7. Substitute L into the second equation to solve for v, then compute L.

Step-by-Step Solution:

Verification / Alternative check:
Pole: 100 m / 50 m/s = 2 s. Bridge: (100 + 250) / 50 = 7 s. Both satisfied.

Why Other Options Are Wrong:
150 m, 120 m, 80 m: Fail one or both equations’ checks.

Common Pitfalls:
Using km/h inadvertently; keep everything in m and s to maintain consistency.

Final Answer:
100 m