Ratio of length of two trains is 4 : 5. Coming from opposite direction, they cross a pole in 4 seconds each . Then in what time will they cross each other .

4  sec.

Ratio of          train 1    :    train 2 

Distance            4        :       5

Speed                4       :       5    ( distance = speed × time , so ratio of distance and speed is same .) 

As both train cross a man in 4 sec . So length of train1 

Distance = Speed × Time 

Length of train 1 = 4R × 4 = 16R

Similarly, legth of train 2 = 5R × 54 = 20R

Total distance = 36R meter 

As trains moves in opposite direction . so relative speed = ( 4 + 5 )R   =  9R m/sec

Time taken by trains to cross each other = \(\frac{36R}{9R}\) = 4 sec .