In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{duration}}\,{\text{of}}\,{\text{the}}\,{\text{flight}}\,{\text{be}}\,x\,{\text{hours}} \cr & {\text{Then}},\frac{{600}}{x} - \frac{{600}}{{x + \left( {1/2} \right)}} = 200 \cr & \Rightarrow \frac{{600}}{x} - \frac{{1200}}{{2x + 1}} = 200 \cr & \Rightarrow x\left( {2x + 1} \right) = 3 \cr & \Rightarrow 2{x^2} + x - 3 = 0 \cr & \Rightarrow (2x + 3)(x - 1) = 0 \cr & \Rightarrow x = 1\,\text{hour} \cr} $$