Multiple choice

A,B and C together complete a work in 3 days. If A or B alone completes that work in 8 days, in what time will C alone complete the same work?

  1. 12 days

  2. 5 days

  3. 2 days

  4. 24 days

  5. None of these
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A Correct answer
Explanation

Let total work = LCM(3, 8) = 24 units. Combined rate of A, B, C = 24/3 = 8 units/day. Rate of A alone = 24/8 = 3 units/day (same as B). Combined rate of A and B = 3 + 3 = 6 units/day. Therefore, C's rate = 8 - 6 = 2 units/day. Time for C alone = 24/2 = 12 days. The distractor 24 days comes from incorrectly adding rates instead of subtracting.

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