Question

A train overtakes two persons walking along a railway track. The first walks at 4.5 km/hr; the second at 5.4 km/hr. The train needs 8.4 and 8.5 seconds to overtake them respectively. What is the speed of the train?

• A. 66 km/hr
• B. 72 km/hr
• C. 71 km/hr
• D. 81 km/hr
• E. 78 km/hr

Hint:

When a train crosses moving objects, the Relative Speed is $(v_{\text{train}} - v_{\text{object}})$ if they move in the same direction.

Answer 1

The Correct Option is D

Step 1: Analyse options.
- Let train speed be $v$ km/hr. - Distance (Train Length) = $(v - 4.5) \times 8.4 = (v - 5.4) \times 8.5$. - $8.4v - 37.8 = 8.5v - 45.9$. - $0.1v = 8.1 \Rightarrow v = 81$.
Step 2: Conclusion.
The speed of the train is 81 km/hr. Final Answer: (d) 81 km/hr