Answer : Option A

Explanation :

Let speed of the train = x kmph and speed of the car = y kmph
Time needed for traveling 600 km if 120 km by train and the rest by car = 8 hr

$MF#%\begin{align}&\Rightarrow \dfrac{120}{x} + \dfrac{(600-120)}{y} = 8\\\\
&\Rightarrow \dfrac{120}{x} + \dfrac{480}{y} = 8 \text{.............(Equation 1)}\\\\
&\Rightarrow \dfrac{15}{x} + \dfrac{60}{y} = 1\text{.............(Equation 1)}\end{align} $MF#%

$MF#%\begin{align}&\Rightarrow \dfrac{200}{x} + \dfrac{(600-200)}{y} = 8\dfrac{20}{60} =8\dfrac{1}{3}=\dfrac{25}{3}\\\\
&\Rightarrow \dfrac{200}{x} + \dfrac{400}{y} = \dfrac{25}{3}\\\\
&\Rightarrow \dfrac{8}{x} + \dfrac{16}{y} = \dfrac{1}{3}\\\\
&\Rightarrow \dfrac{24}{x} + \dfrac{48}{y} = 1\text{.............(Equation 2)}\\\\\\\\
&\text{Solving Equation1 and Equation2}\\\\
&\text{Here Equation1 = Equation2 = 1}\\\\
&\Rightarrow \dfrac{15}{x} + \dfrac{60}{y} = \dfrac{24}{x} + \dfrac{48}{y}\\\\
&\Rightarrow \dfrac{12}{y} = \dfrac{9}{x}\\\\
&\Rightarrow \dfrac{4}{y} = \dfrac{3}{x}\\\\
&\Rightarrow \dfrac{x}{y} = \dfrac{3}{4}\\\\
&\Rightarrow x:y = 3:4\\\\
\end{align} $MF#%