To find the length of the train, we need to analyze the relative motion involved when the train passes the man.

Train Speed Conversion

First, convert the speeds from km/hr to m/s, as the time is given in seconds.

• Train speed ($S_T$): $23.6$ km/hr $= 23.6 \times \frac{5}{18}$ m/s
• Man's speed ($S_M$): $12.4$ km/hr $= 12.4 \times \frac{5}{18}$ m/s

Relative Speed Calculation

Since the train and the man are moving in opposite directions, their speeds add up to determine the relative speed at which the train passes the man.

• Relative speed ($S_{Rel}$) $= S_T + S_M$
• $S_{Rel} = (23.6 + 12.4)$ km/hr $= 36$ km/hr
• Convert relative speed to m/s: $S_{Rel} = 36 \times \frac{5}{18}$ m/s $= 10$ m/s

Train Length Calculation

The time taken for the train to pass the man is the time it takes for the train's length to cross the man's position at the relative speed.

• Let the length of the train be $L$ meters.
• Time to pass the man ($t$) = 11 seconds.
• Using the formula: Distance = Speed × Time
• $L = S_{Rel} \times t$
• $L = 10 \text{ m/s} \times 11 \text{ s}$
• $L = 110 \text{ m}$

The length of the train is 110 meters. The information about passing the platform is not needed for this calculation.