Question:

A man sitting in a train travelling at the rate of 50 km/hr observes that it takes 9 sec for a goods train travelling in the opposite direction to pass him. If the goods train is 187.5 m long, find its speed.

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Use relative speed when solving train problems involving opposite directions. Convert km/hr to m/s using \( \frac{5}{18} \).
Updated On: Mar 7, 2025
  • 25 km/hr
  • 40 km/hr
  • 35 km/hr
  • 36 km/hr
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The Correct Option is A

Solution and Explanation

Let the speed of the goods train be \( x \) km/hr.
Since the trains move in opposite directions, relative speed = \( (50 + x) \) km/hr.
Converting km/hr to m/s: \[ (50 + x) \times \frac{5}{18} \text{ m/s} \] Time taken to pass = 9 sec: \[ \frac{187.5}{(50 + x) \times \frac{5}{18}} = 9 \] \[ 187.5 = 9 \times (50 + x) \times \frac{5}{18} \] \[ 187.5 = \frac{45}{18} \times (50 + x) \] \[ 187.5 = 2.5 \times (50 + x) \] \[ 50 + x = 75 \] \[ x = 25 \text{ km/hr} \] Thus, the speed of the goods train is 25 km/hr.
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