The ratio between the speeds of train J and K is 7:5

Solution

The ratio between the speeds of train J and K is 7:5 respectively. Let’s assume the speed of train J and K is 7y  and 5y respectively. Train J which is (a+140) metre long can cross a pole in 24 seconds. (a+140)/24 = 7y (a+140) = 168y    Eq.(i) If train K can cross a man in 28 seconds. Let’s assume the length of train K is ‘k’. k/5y = 28 k = 140y    Eq.(ii) It is assumed that both of the trains cross each other in (77/3) seconds. [(a+140)+k]/(7y+5y) = (77/3) [(a+140)+k]/(12y) = (77/3) Put Eq.(i) and Eq.(ii) in the above equation. [168y+140y]/(12y) = (77/3) (308y)/(12y) = (77/3) (77/3) = (77/3) We cannot obtain anything from the given information in the question. So the answer cannot be determined.