A train running at $23.6\text{km/hr}$ takes $30$ seconds to pass a platform. Next, it takes $11$ seconds to pass a man walking at $12.4\text{km/hr}$ in the opposite direction. Find the length of the train.

Let the length of the train be $L_{\text{train}}$ meters.
Case 2: Passing the moving man
When the train passes a man moving in the opposite direction, their relative speed is the sum of their speeds.
Speed of train, $v_1=23.6\text{km/hr}$
Speed of man, $v_2=12.4\text{km/hr}$

$$\text{Relative Speed}=v_1+v_2=23.6+12.4=36\text{km/hr}$$

Convert the relative speed into meters per second ($\text{m/s}$):

$$\text{Speed in m/s}=36\times \frac{5}{18}=2\times 5=10\text{m/s}$$

The distance covered while crossing the man is equal to the length of the train ($L_{\text{train}}$).
Given, time taken to cross the man, $t=11\text{seconds}$.

$$L_{\text{train}}=\text{Relative Speed}\times \text{time}$$

$$L_{\text{train}}=10\text{m/s}\times 11\text{s}=110\text{m}$$

Thus, the length of the train is $110\text{m}$.
(Note: The data about the platform in the first sentence is extra information and not needed to find the train's length).