Question

An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?

• A. 36 s
• B. 45 s
• C. 27 s
• D. None of these

Hint:

Use relative speed when two moving objects are involved; actual speed when crossing stationary object.

Answer 1

The Correct Option is A

Relative speed = $(80 - 40) \times \frac{1000}{3600} = 11.11$ m/s. Let length of express = L, goods = 2L. Overtaking time = 54 s $\Rightarrow$ $(L + 2L)/11.11 = 54 \Rightarrow 3L = 600 \Rightarrow L = 200$ m. Crossing 400 m platform: distance = $200 + 400 = 600$ m. Speed = $80 \times \frac{1000}{3600} \approx 22.22$ m/s. Time = $600/22.22 \approx 27$ s → (c).