A and B run a 5 Km race on a round course of 400 m. If their speeds be in the ratio 5 : 4, then how often does the winner pass the other?

41⁄2 times
31⁄2 times
23⁄4 times
21⁄2 times

Correct Answer: 21⁄2 times

Explanation:

When A makes 5 rounds, B makes 4 rounds.
In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time, when A makes 5 rounds.
Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.
In covering 2 Km, A passes B 1 time.
∴ In covering 5 Km, A passes B
= 5 / 2 = 2¹⁄₂ times.

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