In a flight of 6000 km, an aircraft was slowed down due to bad weather. The average speed for the trip was… · ABC26GN3701
Subject: General Aptitude · Chapter: Time and Distance
In a flight of 6000 km, an aircraft was slowed down due to bad weather. The average speed for the trip was reduced by 400 kmph and the time of flight increased by 30 minutes. The original planned duration of the flight was
(a)$2 \frac{1}{2}$ hours
(b)$3 \frac{1}{3}$ hours
(c)$4 \frac{1}{3}$ hours
(d)$5 \frac{1}{3}$ hours
Answer
Answer (as printed): A
Explanation
Let the original planned duration of the flight be $x$ hours. Then, $\frac{6000}{x}-\frac{6000}{\left(x+\frac{1}{2}\right)}=400 \Leftrightarrow \frac{6000}{x}-\frac{12000}{(2 x+1)}=400$ $$\begin{aligned} & \Leftrightarrow \quad \frac{15}{x}-\frac{30}{(2 x+1)}=1 \Leftrightarrow 2 x^{2}+x-15=0 \\ & \Leftrightarrow \quad(x+3)(2 x-5)=0 \Leftrightarrow x=\frac{5}{2}=2 \frac{1}{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.