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

Introduction / Context:
This problem illustrates the situation where a train and a man move in opposite directions. The focus is on using relative speed when motions are towards each other and finding the time required for the train to pass the man completely. It is a standard type of question in aptitude examinations on trains and relative motion.

Given Data / Assumptions:

• Length of the train = 110 m.
• Speed of the train = 60 km/h.
• Speed of the man = 6 km/h.
• The man runs in the direction opposite to the motion of the train.
• We assume constant speeds and straight line motion.

Concept / Approach:
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. To pass the man completely, the train must cover a relative distance equal to its own length. Once we obtain the relative speed in m/s, we can use time = distance / speed to compute the passing time.

Step-by-Step Solution:
Relative speed in km/h = 60 + 6 = 66 km/h. Convert relative speed to m/s: 66 * (5 / 18) = 330 / 18 = 55 / 3 m/s. Distance to be covered relative to the man = length of train = 110 m. Time taken = distance / relative speed = 110 / (55 / 3) = 110 * 3 / 55. Simplify: 110 * 3 / 55 = 6 s.

Verification / Alternative check:
We can reason intuitively. A relative speed of 66 km/h is roughly 18.33 m/s. At that rate, covering 110 m should take about 110 / 18.33 ≈ 6 s, which aligns with the exact calculation. This gives confidence that both unit conversion and arithmetic are correct.

Why Other Options Are Wrong:
Times of 5 s, 7 s, or 10 s do not satisfy the relation time = 110 / (55 / 3). Using these times with the correct relative speed would not yield the correct train length. Only 6 s matches both the given data and the fundamental distance, speed, and time equations.

Common Pitfalls:
A common mistake is to subtract the speeds instead of adding them for opposite direction motion. Another error is mixing units by not converting km/h to m/s when using metres and seconds for distance and time. Following a consistent unit strategy and remembering that opposite direction means speeds add avoids these errors.

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