Question

A train 110 metres long is running with a speed of 60kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

• A. Ssec
• B. 6sec
• C. 10sec
• D. 15sec
• E. 12sec

Answer 1

The Correct Option is B

Step 1: Understand the problem.
A train is 110 meters long and is running at a speed of 60 km/h. A man is running in the opposite direction at 6 km/h. We need to calculate the time it takes for the train to pass the man.

Step 2: Convert the speeds into the same units.
The speed of the train is given as 60 km/h, and the speed of the man is 6 km/h. Since the distance is in meters, we need to convert the speeds into meters per second.
To convert from km/h to m/s, multiply the speed by \( \frac{1000}{3600} = \frac{5}{18} \).
Speed of the train in m/s: \( 60 \times \frac{5}{18} = 16.67 \, \text{m/s} \)
Speed of the man in m/s: \( 6 \times \frac{5}{18} = 1.67 \, \text{m/s} \)

Step 3: Calculate the relative speed.
Since the train and the man are moving in opposite directions, their relative speed is the sum of their individual speeds:
Relative speed = \( 16.67 + 1.67 = 18.34 \, \text{m/s} \)

Step 4: Calculate the time to pass the man.
The time \( t \) taken for the train to pass the man is given by the formula:
\( t = \frac{\text{Distance}}{\text{Speed}} \)
The distance to be covered is the length of the train, which is 110 meters.
So, \( t = \frac{110}{18.34} \approx 6 \, \text{seconds} \)

Step 5: Conclusion.
The time it takes for the train to pass the man is approximately 6 seconds.

Final Answer:
The correct option is (B): 6 sec.