Explanation:

Let's solve the problem to find the speed of the slower train:

- The total length of the two trains is 120 m + 240 m = 360 m.

- When moving in opposite directions, they cross each other in 10 seconds.

- Relative speed (opposite direction):

$$

\text{Relative speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{360 \text{ m}}{10 \text{ s}} = 36 \text{ m/s}

$$

- When moving in the same direction, they cross in 18 seconds.

- Relative speed (same direction):

$$

\text{Relative speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{360 \text{ m}}{18 \text{ s}} = 20 \text{ m/s}

$$

- Let the speed of the slower train be \(v_s\) and the faster train be \(v_f\).

- In opposite directions:

$$

v_f + v_s = 36 \text{ m/s}

$$

- In same direction:

$$

v_f - v_s = 20 \text{ m/s}

$$

By solving these two equations:

- Adding:

$$

2v_f = 56 \Rightarrow v_f = 28 \text{ m/s}

$$

- Subtracting:

$$

v_s = 8 \text{ m/s}

$$

Convert the slower train's speed to km/h:

$$

v_s \text{ in km/h} = 8 \times \frac{18}{5} = 28.8 \text{ km/h}

$$

- Option 2: 28.8 km/h