It takes 15 seconds for a train travelling at 60 km/hour to cross entirely another train half its length and travelling in opposite direction at 48 km/hour. It also passes a bridge in 51 seconds. The length of the bridge is

Speed of train 1 = 60 km/hr = 50/3 m/s
Speed of train 2 = 48 km/hr = 40/3 m/s
Thus, their relative speed = 90/3 = 30 m/s
Let, Length of train 1 = l
Thus, the length of train 2 will be 0.5 l
Time taken by them to cross each other = 15 s
Thus, $$ 15*30 = 1.5l$$
Thus, $$ l = 300 $$
Train 1 takes 51s to cross a bridge
Let the length of the bridge be b
Thus, $$\frac{50*51}{3} = 300+b $$
Hence, $$ 850 = 300+b $$
Hence, $$b = 550$$ m
Thus, option A is the correct answer.