Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in:

Let length of each train be x meter.
Then, speed of 1^st train = $$\frac{x}{{18}}$$ m/sec
Speed of 2^nd train = $$\frac{x}{{12}}$$ m/sec
Now,
When both trains cross each other, time taken
$$\eqalign{ & = {\frac{{2x}}{{ { {\frac{x}{{18}}} + {\frac{x}{{12}}} } }}} \cr & = \frac{{2x}}{{ {\frac{{ {2x + 3x} }}{{36}}} }} \cr & = \frac{{2x \times 36}}{{5x}} \cr & = \frac{{72}}{5} \cr & = 14.4\,\,{\text{seconds}} \cr} $$