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assuming average times over the race, doesn't A) indicate that X was two laps ahead of Y? thus, meaning that X had finished 10,000 meters, whereas Y had only finished 9,200 meters? so isn't the ratio of time the same as the ratio of distance? thus the ratio of Y to X was 9200 to 10000, or 23/25?

well, we know that while X (first runner) completed 25 laps, Y (second runner) completed 23 laps. Hence, in the same time, one completed 10,000, while the other completed 9,200. I think, we can pick any time for T here and get the relationship of t1 to t2.
hence I'd go for D

From the question, we know they need to do 10,000/400=25 laps

From (2), X takes 60*25 = 1500 seconds, and Y takes 62.4*25 = 1560 seconds
With this in hand, (2) is sufficient.

Now we need to consider (1).
When X finishes 25 laps, he lapped Y for the second time. This means he is 800 meters ahead.
All we have is information about the distance X and Y have already ran, but nothing about their speed, and so we can conclude the time they took and hence the ratio of their time.
Therefore (1) is not sufficient.

I think what is tricky whith statement 1 is that we do not know how much time will need Y to complete the 2 remaining laps after he was crossed by X.

I would also choose B

Wow! I choose D considering that Y travels at a constant speed. Good catch.

Just for discussion, If the question is:
Two Runners, X and Y, competed in a 10000 m run. The race took place in a oval track 400m long. What is tha ration od X's time to Y's time, if they run at constant speed? (1) Just a X crossed the finish line, he lapped Y for the second time. (2) X averaged 60s per lap, and Y averaged 62.4 s per lap.