Train A leaves station M at 7:30 AM and reaches station N at 2:30 PM on the same day. Train B leaves station N at 9:30 AM and reaches station M at 2:30 PM on the same day. Find the time when Trains A and B meet.

Correct option is A

Given:

Train A: Departs M at 7:30 AM, arrives N at 2:30 PM.
Total travel time = 7 hours.

Train B: Departs N at 9:30 AM, arrives M at 2:30 PM.
Total travel time = 5 hours.

Concept Used:

Relative Speed Concept: Distance covered is proportional to time taken.

Solution:

Let the distance between M and N = D.

Speed of A =$$\frac{D}{7}.$$​​

Speed of B $$= \frac{D}{5}.$$​​

By 9:30 AM, Train A has already traveled 2 hours.

Distance covered =$$2 \times \frac{D}{7} = \frac{2D}{7}.$$​​

Remaining distance =$$D - \frac{2D}{7} = \frac{5D}{7}.$$​​

 From 9:30 AM onward, both trains travel towards each other.

 Relative speed $$= \frac{D}{7} + \frac{D}{5} = \frac{12D}{35}.$$​​

Time to meet after 9:30 AM =

$$\frac{\text{Remaining Distance}}{\text{Relative Speed}} = \frac{\tfrac{5D}{7}}{\tfrac{12D}{35}} = \frac{5}{7} \times \frac{35}{12} = \frac{25}{12} \text{ hours} = 2 \text{ hours 5 minutes}.$$​

Meeting time = 9:30 AM + 2h 5m = 11:35 AM