A 600 m long train is moving at 67 km/h and overtakes a man walking at 7 km/h in the same direction of the train. How many seconds does the train take to completely cross the man?

Introduction / Context:
This numerical aptitude question involves a train overtaking a man walking in the same direction. It tests the concept of relative speed when two objects move along the same line in the same direction and asks for the time taken to completely cross the man.

Given Data / Assumptions:

• Length of the train = 600 m.
• Speed of the train = 67 km/h.
• Speed of the man = 7 km/h.
• They move in the same direction along the track.
• We assume constant speeds and straight track.

Concept / Approach:
When two objects move in the same direction, the effective relative speed is the difference of their speeds. The train needs to cover a distance equal to its own length relative to the man in order to completely cross him. We convert speeds from km/h to m/s, compute the relative speed, and then use time = distance / speed to find the crossing time in seconds.

Step-by-Step Solution:
Step 1: Relative speed in km/h = 67 - 7 = 60 km/h. Step 2: Convert 60 km/h to m/s using factor 5/18. Step 3: Relative speed = 60 * 5 / 18 = 50 / 3 m/s. Step 4: Distance to be covered relative to the man = length of train = 600 m. Step 5: Use time = distance / speed, so time = 600 / (50 / 3). Step 6: Time = 600 * 3 / 50 = 1800 / 50 = 36 seconds.

Verification / Alternative check:
Check using a quick mental method. Relative speed 50 / 3 m/s is approximately 16.67 m/s. If time were 36 seconds, distance covered would be 16.67 * 36, which is very close to 600 m, matching the train length. This confirms that the train needs 36 seconds to completely cross the man.

Why Other Options Are Wrong:

• 29 seconds: At this time, distance covered would be less than 600 m, so the train would not have fully passed the man.
• 58 seconds: This time is too large and would imply the train has travelled much more than its own length relative to the man.
• 44 seconds: This is also larger than necessary and does not match the exact distance calculation.

Common Pitfalls:
Typical mistakes include adding the speeds instead of subtracting them for motion in the same direction and forgetting to convert km/h into m/s. Another common error is to use the total path length instead of the train length when a train is crossing a man or pole, where only the train length matters.

Final Answer:
The train takes 36 seconds to cross the man completely.