Two train having equal length cross a pole in 7 sec and 9 sec respectively . Running in opposite direction in what time will they cross each other ?

7\(\frac{7}{8}\) sec

Ratio of          train 1    :    train 2 

Time                 7        :       9

Speed                9       :       7   ( distance = speed × time , so ratio of time and speed is inverse .)

Distance = Speed × Time 

Length of train 1 = 9R × 7 = 63R

Similarly, legth of train 2 = 7 × 9R = 63R

Total distance = 126R  meter 

As trains moves in opposite direction . so relative speed = ( 7 + 9 )R   =  16R m/sec

Time taken by trains to cross each other = \(\frac{126R}{16R}\) =  7\(\frac{7}{8}\) sec.