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:
A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hours
Answer: Option A
Solution (By Examveda Team)
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{duration}}\,{\text{of}}\,{\text{the}}\,{\text{flight}}\,{\text{be}}\,x\,{\text{hours}} \cr & {\text{Then}},\frac{{600}}{x} - \frac{{600}}{{x + \left( {1/2} \right)}} = 200 \cr & \Rightarrow \frac{{600}}{x} - \frac{{1200}}{{2x + 1}} = 200 \cr & \Rightarrow x\left( {2x + 1} \right) = 3 \cr & \Rightarrow 2{x^2} + x - 3 = 0 \cr & \Rightarrow (2x + 3)(x - 1) = 0 \cr & \Rightarrow x = 1\,\text{hour} \cr} $$This Question Belongs to Arithmetic Ability >> Speed Time And Distance
The answer is 1.5 hour please check your answer
Examveda
Let,the speed of flight = x km/hr
So,
600/(x-200) - 600/x = 1/2
=> (x-x+200)/x(x-200) = 1/1200
=> 1/(x^2-200x) = 1/1200*200
=> x^2 - 200x - 400*600 = 0
=> (x+400)(x-600) = 0
=> x = 600 km/hr
Duration of flight = 600km/600km/hr = 1hr
Let,the speed of flight = x km/hr
So,
600/(x-200) - 600/x = 1/2
=> (x-x+200)/x(x-200) = 1/1200
=> 1/(x^2-200x) = 1/1200*200
=> x^2 - 200x - 400*600 = 0
=> (x+400)(x-600) = 0
=> x = 600 km/hr
Duration of flight = 600km/600km/hr = 1hr