UPSC 2015 CDS I Math Paper

Let the original speed of the aircraft be x km/hr
Therefore, duration of the flight=

600

x

hr
Time taken by the aircraft at reduced speed = Time taken by the aircraft at original speed + 30 minutes
∴

600

x−200

−

600

x

=

30

60

⇒

120000

x(x−200)

=

1

20

⇒x2−200x−240000=0
⇒x2−600x+400x−240000=0
⇒(x−600)(x+400)=0
⇒x=600‌or‌x=−400
But, the speed cannot be negative. So,x=600km/hr
Therefore, the duration of the flight=

600

600

=1hr