Multiple choice

A, B and C can individually complete a work in 10, 20 and 30 days respectively. If they work on alternate days starting with C then B and A (i.e., Day1: C, Day2: B, Day3: A, Day4: C, ...), in how many days will the work be completed?

  1. 17 days

  2. 18 days

  3. 16 days

  4. 15 days
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A Correct answer
Explanation

Work rates: A=1/10, B=1/20, C=1/30. Cycle (C, B, A): 1/30 + 1/20 + 1/10 = (2+3+6)/60 = 11/60. In 15 days (5 cycles), work done = 5 * 11/60 = 55/60. Remaining = 5/60 = 1/12. Day 16 (C): 1/30 done. Day 17 (B): 1/20 done. Total work is completed on day 17.

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