A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Step 1: Understand the given information

• Length of the train = 125 meters
• Speed of the man = 5 km/h
• The train passes the man in 10 seconds
• Both are moving in the same direction

Step 2: Use relative speed concept

Since the train and the man are moving in the same direction, we subtract the man's speed from the train's speed to get the relative speed.

Let the speed of the train be x km/h.

Relative speed = (x - 5) km/h = ((x - 5) × 1000) / 3600 m/s

Step 3: Use the formula: Distance = Speed × Time

Distance = 125 meters

Time = 10 seconds

Speed = Distance / Time = 125 / 10 = 12.5 m/s

Step 4: Solve for x

(x - 5) × 1000 / 3600 = 12.5

(x - 5) = (12.5 × 3600) / 1000

(x - 5) = 45

x = 50 km/h

Answer: 50 km/h

The speed of the train is 50 kilometers per hour.

This problem tests the understanding of relative speed in the same direction. Since the man and the train move in the same direction, the train takes longer to overtake him, and the effective speed is reduced. The use of basic distance = speed × time formula allows solving such problems efficiently.