CAT 2003 Question Paper (Leaked) Question 67

Question 67

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 the 5th 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?


Let A , B and f,s be the distance traveled and speed of the fastest and the slowest person respectively. Also f=2s so in the given time A=2B. Since the ration of the speeds is 2:1, they will meet at 2-1 points = 1 pont.

Both meet each other for first time at starting point . let b travel distance equal to 1 circumference i.e. 1000m so A=2000m . Both meet after 5 min so speed of slowest is 1000/5=200m/min . So speed of the fastest is 400m/min. So time taken by A to complete race 4000/400 = 10 min

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