A train is 110 meters long and runs at 60 km/h. In how many seconds will it completely pass a man who is running at 6 km/h in the direction opposite to that of the train?

Introduction / Context:
This question involves relative speed between a moving train and a man on the track. The train and the man are moving in opposite directions, and we need to determine the time taken for the train to pass the man completely.

Given Data / Assumptions:
- Length of the train is 110 meters.
- Speed of the train is 60 km/h.
- Speed of the man is 6 km/h.
- The man runs in the direction opposite to the direction of the train.
- We must find the time taken in seconds for the train to pass the man.

Concept / Approach:
When two objects move in opposite directions, their relative speed is the sum of their speeds. The time required for the train to completely pass the man equals the length of the train divided by the relative speed, with all units consistent. So we convert relative speed from km/h to m/s and then apply the formula time = distance / speed.

Step-by-Step Solution:
Step 1: Compute the relative speed since directions are opposite: 60 km/h + 6 km/h = 66 km/h.Step 2: Convert 66 km/h to meters per second by multiplying by 5 / 18.Step 3: Relative speed in m/s = 66 * 5 / 18 = 330 / 18 = 55 / 3 m/s.Step 4: The distance to be covered for complete passing is the length of the train, which is 110 meters.Step 5: Time = distance / speed = 110 / (55 / 3) seconds.Step 6: Simplify the fraction: 110 * 3 / 55 = 330 / 55 = 6 seconds.Step 7: Thus, the train passes the man completely in 6 seconds.

Verification / Alternative check:
We can approximate the relative speed numerically. 66 km/h is approximately 18.33 m/s. Dividing the train length 110 meters by 18.33 m/s gives about 6 seconds. This confirms the exact calculation of 6 seconds.

Why Other Options Are Wrong:
10 or 8 seconds would arise if one incorrectly used only the train speed or subtracted the man's speed instead of adding. 4 seconds would require a much higher relative speed than actually present. 12 seconds comes from treating the man as stationary with half the actual relative speed. Only 6 seconds correctly matches the relative speed calculation.

Common Pitfalls:
Typical mistakes include subtracting speeds when directions are opposite, failing to convert km/h to m/s, or using the sum of speeds but not converting units properly. Forgetting that only the train length is relevant for passing a point or a person is another frequent error.

Final Answer:
The train will completely pass the man in 6 seconds.