It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is:

Let the speed of train = $$x$$ km/hr and speed of car = $$y$$ km/hr

Total distance = 600 km

Using, time = distance/speed

If 120 km is done by train and the rest by car,

=> Time = $$\frac{120}{x}+\frac{480}{y}=8$$

=> $$\frac{15}{x}+\frac{60}{y}=1$$

=> $$\frac{1}{x}+\frac{4}{y}=\frac{1}{15}$$ ----------(i)

Similarly, $$\frac{200}{x}+\frac{400}{y}=8\frac{1}{3}=\frac{25}{3}$$

=> $$\frac{24}{x}+\frac{48}{y}=1$$

=> $$\frac{1}{x}+\frac{2}{y}=\frac{1}{24}$$ ----------(ii)

Subtracting equation (ii) from (i), we get :

=> $$\frac{2}{y}=\frac{1}{15}-\frac{1}{24}=\frac{3}{120}$$

=> $$y=\frac{240}{3}=80$$ km/hr

Substituting it in equation (ii), => $$\frac{1}{x}=\frac{1}{24}-\frac{1}{40}=\frac{5-3}{120}$$

=> $$x=\frac{120}{2}=60$$ km/hr

$$\therefore$$ Ratio of the speed of the train to that of the car = $$\frac{x}{y}$$

= $$\frac{60}{80}=\frac{3}{4}$$

=> Ans - (B)