Answer : Option D

Explanation :

Let the duration of the flight = x hours
Given that distance = 600 km

$MF#%\begin{align}
&\text{Speed = }\dfrac{\text{Distance}}{\text{Time}}=\dfrac{600}{x}\text{................(Equation1)}\\\\
&\text{Duration of the flight due to the slow down = }(x + \dfrac{30}{60})\text{ hours} = (x + \dfrac{1}{2})\text{ hours}\\\\
&\text{New speed = }\dfrac{600}{(x + \dfrac{1}{2})}\text{................(Equation2)}\\\\
&\text{From Equations 1 and 2, Reduction in Speed =}\dfrac{600}{x} - \dfrac{600}{(x + \dfrac{1}{2})}\\\\
&\text{Given that Reduction in average speed =}200\text{ km/hr }\\\\
&\Rightarrow \dfrac{600}{x} - \dfrac{600}{(x + \dfrac{1}{2})} = 200\\\\
&\Rightarrow \dfrac{3}{x} - \dfrac{3}{(x + \dfrac{1}{2})} = 1\\\\
&\Rightarrow \dfrac{3}{x} - \dfrac{6}{2x + 1} = 1\\\\
&\Rightarrow \dfrac{3(2x+1) - 6x}{x(2x+1)} = 1\\\\
&\Rightarrow \dfrac{6x + 3 - 6x}{x(2x+1)} = 1\\\\
&\Rightarrow \dfrac{3}{x(2x+1)} = 1\\\\
&\Rightarrow 2x^2 + x - 3 = 0 \text{................(Equation3)}\\\\
&\text{From here, you can get the answer using Trial and error method.}\\
&\text{If you try with the values given as the choices, you can see the value of x = 1}\\
&\text{satisfies the equation 3. Hence answer is 1 hour}\\\\
&\text{Or, we can solve the equation 3 to get the answer}\\\\
&\Rightarrow 2x^2 + x - 3 = 0\\\\
&\Rightarrow (2x + 3)(x - 1) = 0\\\\
&\Rightarrow x = 1 \text{(Removing the -ve value for x)}\\\\
&\text{Hence answer is 1 hour}
\end{align} $MF#%