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In a race of 1000 m, A beats B by 150 m, while in another race of 3000 m, C beats D by 400 m. Speed of B is equal to that of D. (Assume that A, B, C and D run with uniform speed in all the events). If A and C participate in a race of 6000 m, then which one of the following is correct?

In a race of 1000 m, A beats B by 150 m, while in another race of 3000 m, C beats D by 400 m. Speed of B is equal to that of D. (Assume that A, B, C and D run with uniform speed in all the events). If A and C participate in a race of 6000 m, then which one of the following is correct? Correct Answer A beats C by 115.38 m

Suppose the speed of B = speed of D = ‘x’ m/sec.

In the race of 1000 m, A beats B by 150 m,

⇒ Distance covered by B = 1000 – 150 = 850 m

∵ Time taken by both participants will be equal,

⇒ Time taken = 1000/(Speed of A) = 850/x

⇒ Speed of A = (20x/17) m/sec.

Similarly, in race of 3000 m, C beats D by 400 m,

⇒ Distance covered by D = 3000 – 400 = 2600 m

⇒ Time taken = 3000/(Speed of C) = 2600/x

⇒ Speed of C = (15x/13) m/sec.

Now, in the race of 6000 m,

∵ Speed of A > Speed of C

This means that A will win the race,

⇒ Time taken by A to complete the race = 6000/(20x/17) = (5100/x) sec.

⇒ Distance covered by C in the same time = (15x/13) × (5100/x) = 5884.62 m

∴ In race of 6000 m, A beats C by = 6000 – 5884.62 = 115.38 m

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