A train leaves Hyderabad at 4:00 A.M. and reaches Vijayawada at 8:00 A.M. the same day. Another train leaves Vijayawada at 6:00 A.M. and reaches Hyderabad at 9:30 A.M the same day. At what time do the two trains cross each other?

Time taken by the first train (Hyderabad to Vijayawada) = 4:00 A.M. to 8:00 A.M. = $4$ hours.Time taken by the second train (Vijayawada to Hyderabad) = 6:00 A.M. to 9:30 A.M. = $3.5$ hours = $\frac{7}{2}$ hours.Let the total distance between Hyderabad and Vijayawada be the LCM of $4$ and $\frac{7}{2}$, which is $28\text{ km}$.Speed of the first train ($S_1$) = $\frac{28}{4}=7\text{ km/h}$.Speed of the second train ($S_2$) = $\frac{28}{7/2}=8\text{ km/h}$.By 6:00 A.M., the first train has already traveled for $2$ hours (from 4:00 A.M. to 6:00 A.M.).Distance covered by the first train in $2$ hours = $7\times 2=14\text{ km}$.Remaining distance at 6:00 A.M. = $28-14=14\text{ km}$.At 6:00 A.M., both trains are moving towards each other.Relative speed = $S_1+S_2=7+8=15\text{ km/h}$.Time taken to meet after 6:00 A.M.:
$$\text{Time}=\frac{\text{Remaining Distance}}{\text{Relative Speed}}=\frac{14}{15}\text{ hours}$$
Converting to minutes:
$$\frac{14}{15}\times 60=56\text{ minutes}$$
So, they cross each other at 6:00 A.M. + 56 minutes = 6:56 A.M.