CAT 2003 | Question: 1-120

Question

In a $4000$ meter race around a circular stadium having a circumference of $1000$ meters, the fastest runner and the slowest runner reach the same point at the end of $5$th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

• A. $20$ min
• B. $15$ min
• C. $10$ min
• D. $5$ min

Answer 1

let slowest runner speed be x m/s

so fastest runner speed=2x

Their Relative speed=x,They meet in 5mins

300x=1000

x=10/3

therefore fastest runner speed=2x=20/3m/s

Timetaken by him to finish Race

=4000/(20/3)

=600 sec=10min