Subject: General Aptitude · Chapter: Time and Distance · Exam: 2006 · Marks: · Difficulty:
An aeroplane started 30 minutes later than the scheduled time from a place 1500 km away from its destination. To reach the destination at the scheduled time the pilot had to increase the speed by 250 km/hr. What was the speed of the aeroplane per hour during the journey?
Answer
Answer (as printed):
Explanation
Let the original speed of the aeroplane be $x$ km/hr. $\therefore \frac{1500}{x}-\frac{1500}{(x+250)}=\frac{1}{2} \Leftrightarrow 3000(x+250)-3000x=x(x+250) \Leftrightarrow x^{2}+250x-750000=0 \Leftrightarrow x^{2}+1000x-750x-750000=0 \Leftrightarrow x(x+1000)-750(x+1000)=0 \Leftrightarrow (x+1000)(x-750)=0 \Leftrightarrow x=750$. Hence, speed of the aeroplane during the journey $=(750+250)$ km/hr $=1000$ km/hr.
Explanation as extracted from the printed page; notation may be imperfect.