A train 100m long takes 9 seconds to cross a man walking at 5 km/hr in the…

The correct answer is Option D: 35 km/hr.

Step-by-Step Solution

1. Define Variables: Let the speed of the train be x km/hr. Since the man is walking in the opposite direction at 5 km/hr, their relative speed is (x + 5) km/hr.

2. Convert Speed to Meters per Second (m/s): Convert the relative speed from km/hr to m/s by multiplying by 5/18.

   • Relative speed in m/s = (x + 5) * (5/18).

3. Use the Time-Distance Formula: Time = Distance / Speed. Here, the distance is the length of the train (100 m) and the time is 9 seconds.

   • 9 = 100 / ((x + 5) * (5/18))

   • 9 = (100 * 18) / ((x + 5) * 5)

   • 9 = 1800 / (5 * (x + 5))

   • 9 = 360 / (x + 5)

4. Solve for x:

   • 9 * (x + 5) = 360

   • x + 5 = 360 / 9

   • x + 5 = 40

   • x = 35 km/hr.