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

• (a) 45 km/hr
• (b) 50 km/hr
• (c) 54 km/hr
• (d) 55 km/hr

To find the speed of the train, we first need to determine the relative speed between the train and the man. Since both are moving in the same direction, we can use the following steps:

Step 1: Convert the man's speed

The man's speed is given as 5 km/hr. To work with consistent units, we convert this speed into meters per second:

• 5 km/hr = (5 * 1000 m) / (3600 s) = 1.39 m/s

Step 2: Calculate the relative speed

The train passes the man in 10 seconds while covering its entire length of 125 meters. The relative speed of the train with respect to the man can be calculated using the formula:

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

Step 3: Determine the train's speed

The relative speed is the speed of the train minus the speed of the man:

• Speed of Train = Relative Speed + Speed of Man
• Speed of Train = 12.5 m/s + 1.39 m/s = 13.89 m/s

Step 4: Convert the train's speed to km/hr

Now, we convert the train's speed back to kilometers per hour:

• Speed in km/hr = 13.89 m/s * (3600 s / 1000 m) = 50 km/hr

Final Answer

The speed of the train is 50 km/hr, which corresponds to option (b).