Ratio of length of two trains is 5 : 7. 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            5        :       7

Speed                5       :       7    ( 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 = 5R × 5 = 25R

Similarly, legth of train 2 = 7R × 5 = 35R

Total distance = 60R meter 

As trains moves in opposite direction . so relative speed = ( 7 + 5 )R   =  12R m/sec

Time taken by trains to cross each other = \(\frac{60R}{12R}\) = 5 sec .