A train of length 200 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

Step 1: Convert all the units to a common unit. Here, we will convert everything to meters and seconds because the length of the train is given in meters and time is given in seconds.

The speed of the man is given in km/hr. We know that 1 km = 1000 meters and 1 hour = 3600 seconds. So, 10 km/hr = 10 * 1000 meters/3600 seconds = 2.78 meters/second.

Step 2: The train crosses the man in 10 seconds. This means the train travels a distance equal to its own length in this time, which is 200 meters.

Step 3: The speed of an object is defined as the distance it travels divided by the time it takes to travel that distance. So, the speed of the train relative to the man is 200 meters / 10 seconds = 20 meters/second.

Step 4: However, this is the relative speed of the train with respect to the man who is also moving. The actual speed of the train is the relative speed plus the speed of the man. So, the actual speed of the train is 20 meters/second + 2.78 meters/second = 22.78 meters/second.

Step 5: Convert this speed back to km/hr for the final answer. We know that 1 meter/second = 3.6 km/hr. So, 22.78 meters/second = 22.78 * 3.6 km/hr = 82 km/hr.

So, the speed of the train is 82 km/hr.