A train leaves Station X at 5 a.m. and reaches Station Y at 9 a.m. Another train leaves Station Y at 7 a.m. and reaches Station X at 10.30 a.m. At what time do the two trains cross each other?

Time taken by first train = 4 hours and time taken by second train = 3.5 hours

Since, distance travelled for both is same, ratio of time = $$8:7$$

=> Ratio of speeds of both trains (speed is inversely proportional to time) = $$7:8$$ respectively.

Let speed of first train be $$7x$$ km/hr and speed of second train be $$8x$$ km/hr and thus total distance between two stations = $$28x$$ km

Thus, distance travelled by first train in first two hours (till second train starts) = $$14x$$ km

=> Remaining distance between the trains at 7 am = $$14x$$ km and relative speed coming in opposite directions = $$7x+8x=15x$$ km/hr

Time taken for them to meet each other = $$\frac{14x}{15x}=\frac{14}{15}\times60=56$$ minutes

$$\therefore$$ The two trains will meet at 7:56 am

=> Ans - (B)