Let T be the time they'll meet for the first time. So, the distance A,B and C will run before meeting is 10T, 20T and 30T, respectively. The only place they can meet at is the start point. So, T must satisfy these conditions:
1000a = 10T, 1000b = 20T, 1000c = 30T,
where a,b,c are the number of laps A, B and C have to take before they met. We see that the minimum time to satisfy this condition is 100 seconds. By this time, A, B and C will take 1, 2 and 3 laps respectively.
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