Ratio of length of two trains is 2 : 3. Coming from opposite direction, they cross a pole in 5 seconds each . Then in what time will they cross each other .

5 sec.

Ratio of          train 1    :    train 2 

Distance            2        :       3

Speed                2       :       3    ( distance = speed × time , so ratio of distance and speed is same .) 

As both train cross a man in 5 sec . So length of train1 

Distance = Speed × Time 

Length of train 1 = 2R × 5 = 10R

Similarly, legth of train 2 = 3R × 5R = 15R

Total distance = 25R meter 

As trains moves in opposite direction . so relative speed = ( 2 + 3 )R   =  5R m/sec

Time taken by trains to cross each other = \(\frac{25R}{5R}\) = 5 sec .