The speed of a train is 3 times that of a car and 1.5 times that of a steamer. A person travelled by x km by steamer, 3.75 x km by train and $$\frac{x}{2}$$ km by car. If the speed of the car is 40 km/h and total time take by him is $$4\frac{1}{2}$$ hours, then the total distance traveled by him in three modes is:

Speed of Car = 40 km/hr

Speed of train is 3 times the speed of car and 1.5 times of speed of streamer = 40$$\times\ 3=120$$ km/hr

Speed of streamer = $$\frac{120}{1.5}=80\ $$ km/hr

As we know, 

Speed = $$\frac{dis\tan ce}{time\ }$$

Distance travelled by car, train and streamer is x/2 km, 3x km and x km respectively.

According to question,

 $$\frac{x}{80}+\frac{3.75x}{120}+\frac{x}{80}=4.5$$

$$\frac{3x+7.5x+3x}{240}=4.5$$

$$x\ =\ 80\ $$

Total distance = 3.75x + x + x/2 = 5.25 x

= $$5.25\times\ 80=420\ km$$

Hence, Option D is correct.