A train X travelling at 72 km/h crosses another train Y travelling at 63 kmph in opposite direction in 18 seconds. If the length of train Y is two third the length of the X, then find the length of the X?

Trains X and Y move in opposite directions, so relative speed = 72 + 63 = 135 km/h = 135 × 5/18 = 37.5 m/s. Distance covered in 18 seconds = 37.5 × 18 = 675 m = sum of both train lengths. Let Lx be length of X, then Ly = (2/3)Lx. So Lx + (2/3)Lx = 675, (5/3)Lx = 675, Lx = 405 m. The key concepts are converting relative speed to m/s and understanding that crossing time depends on combined lengths.