CAT 2003 Slot 1 — QA Question 20
Answer the following question based on the information given below.
A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east endpoint of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and km/hr on all the chord roads.
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?
Answer & solution
- A
20 min
- B
15 min
10 min
- D
5 min
Let the speed of the slowest runner be s m/min and the speed of the fastest runner be 2s m/min.
Length of the race track = 1000 m and the two runners meet after 5 minutes.
∴ Relative speed = 1000/5 = 200 m/min
∴ 2s − s = 200
∴ s = 200 m/min
∴ The speed of the fastest runner = 2s = 400 m/min
∴ The time taken by the fastest runner to complete the race = 4000/400 = 10 min
Hence, option (c).
Alternatively,
The slowest runner covers 500 m when the fastest runner covers 1000 m.
∴ The two meet at the starting point when the fastest runner covers 2000 m and the slowest runner covers 1000 m.
∴ The fastest runner runs 2000 m in 5 minutes.
∴ He runs 4000 m in 10 minutes.
Hence, option (c).