UPSC 2016 CDS I Math Paper

Let the original average speed of the cyclist be x km/hour. Time taken by the cyclist at the reduced average speed - Time taken by the cyclist at the original average speed = 20 minutes
∴

14

x−1

−

14

x

=

20

60

⇒

14

x(x−1)

=

1

3

⇒x2−x−42=0
⇒(x−7)(x+6)=0
⇒x=7
(Speed of the cyclist cannot be negative)
Thus, the original average speed of the cyclist is 7 km/hour.