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 cars is:

2 : 3

3 : 2

3 : 4

4 : 3

Explanation:

Let the speed of the train be $ x $ km/hr and that of the car be $ y $ km/hr.

Then,$ \dfrac{120}{x} $+$ \dfrac{480}{y} $= 8 $\Rightarrow \dfrac{1}{x} $+$ \dfrac{4}{y} $=$ \dfrac{1}{15} $....(i)

And,$ \dfrac{200}{x} $+$ \dfrac{400}{y} $=$ \dfrac{25}{3} $ $\Rightarrow \dfrac{1}{x} $+$ \dfrac{2}{y} $=$ \dfrac{1}{24} $....(ii)

Solving (i) and (ii), we get: $ x $ = 60 and $ y $ = 80.

$\therefore$ Ratio of speed = 60 : 80 = 3 : 4.