A, B and C start running simultaneously from point P, Q and R respectively on a circular track. The distance between any two of the three points P, Q and R is L and the ratio of the speeds of A, B and C are 1:2:3. If A and B run in opposite directions while B and C run in the same direction, what is the distance run by A before A, B and C meet for the 3rd time?
Options:
A. 10 L
B. A, B and C never meet
C. 403L
D. 12L
E. 100

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Answer: Option B
: B

Option (b) A, B, C are separated by distance L each from each other. For all of them to meet, A should meet B and C at the meeting point of B and C. If we assume that C takes 3 units of time to cover the whole circle once, then B and C meets at the point R for the 1sttime after 3 units of time. Then they keep meeting at the same point 9 units of time. That is at times 3, 12, 21 etc. But A will reach R for the 1st time 6 units of time after the start and keeps doing that after every 9 units of time after that. That is at times 6, 15, 24 etc.

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