Train A leaves station M at 7:35 AM and reaches station N at 2:35 PM on the same day.Train B leaves station N at 9:35 AM and reaches station M at 2:35 PM on the same day.Find the time when Trains A and B meet.

Correct option is C

Given:

Train A leaves station M at 7:35 AM and reaches station N at 2:35 PM.

Train B leaves station N at 9:35 AM and reaches station M at 2:35 PM.

We need to find the time when Train A and Train B meet.

Formula Used: ​

Time = $$\frac{\text{Distance}}{\text{Speed}}$$​​

Solution:

Train A's total travel time = 7 hours.

Train B's total travel time = 5 hours

So, Train A travels for 2 hours before Train B starts.

This means that at 9:35 AM, Train A has already covered part of the distance.

Distance covered by Train A before 9:35 AM:

Since Train A travels for 2 hours, it covers a part of the total distance, i.e.,$$\frac{2}{7}$$​ of the total distance.

The remaining distance when Train B starts at 9:35 AM is $$\frac{5}{7}$$​ of the total distance. From this point onward, both trains are moving towards each other.

Time to meet = $$\frac{\frac{5}{7}}{\frac{1}{7} + \frac{1}{5}}$$​​

​$$= \frac{\frac{5}{7}}{\frac{5+7}{35}}$$​​

​$$= \frac{5}{7} \times \frac{35}{12}$$​​

​$$= \frac{25}{12} \text{ hours} \\ \ \\= 2 \text{ hours and } 5 \text{ minutes}$$​​

Time when they meet:

Train B starts at 9:35 AM

= 9 : 35 AM + 2hours 5minutes = 11 : 40 AM

Alternate Solution: ​

For the first two hours A covers 

= 5 $$\times$$ 2 = 10

remaining distance = 35 - 10 = 25 

Now, Relative speed (opposite direction) = 5 + 7 = 12 

Time to meet = $$\frac{25}{12} = 2 \ \text{hours} \ 5 \ \text{min.}$$ 

Train B starts at 9:35 AM

= 9 : 35 AM + 2hours 5minutes = 11 : 40 AM