Train A leaves station X at 09:30 hours and reaches station Y at 13:30 hours. Train B leaves station Y at 11:30 hours and reaches station X at 15:00 hours. Assuming that the two trains travel at constant speeds, at what time do the two trains cross each other?

Correct option is C

Given:
Train A leaves station X at 09:30 and reaches Y at 13:30 → Travel time = 4 hours
Train B leaves station Y at 11:30 and reaches X at 15:00 → Travel time = 3.5 hours
Both trains travel at constant speeds
We are to find the time when the two trains cross each other

Solution:

$$\text{Let the total distance between stations X and Y be } D. \\\text{Train A: Speed} = \frac{D}{4}, \quad \text{Train B: Speed} = \frac{D}{3.5} = \frac{2D}{7} \\\ \\\text{Train A travels alone from 09:30 to 11:30 (2 hours):} \\\text{Distance covered} = \frac{D}{4} \times 2 = \frac{D}{2} \\\ \\\text{Let } t \text{ be the time (in hours) after 11:30 when they meet.} \\\left( \frac{D}{4} + \frac{2D}{7} \right) t = \frac{D}{2} \\\ \\\frac{15D}{28} t = \frac{D}{2} \\\ \\\Rightarrow \frac{15}{28} t = \frac{1}{2} \\\ \\\Rightarrow t = \frac{1}{2} \times \frac{28}{15}\\ = \frac{14}{15} \text{ hours} \\\ \\\text{Convert to minutes: } \frac{14}{15} \times 60 = 56 \text{ minutes} \\\ \\\text{So, they meet at } 11{:}30 + 56 \text{ minutes } = \boxed{12{:}26}$$

​Final Answer:
Trains meet 56 minutes after 11:30
That is at 12:26 PM