Multiple choice

A, B and C can do a work in 36, 72 and 54 days respectively. They started the work together but A left 8 days before the completion of the work and C left 12 days before the completion of the work. In how many days was the work completed?

  1. 21

  2. 20

  3. 24

  4. 25

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total work = LCM(36, 72, 54) = 216 units. A's rate = 6/day, B's rate = 3/day, C's rate = 4/day. A worked for (d-8) days, C worked for (d-12) days, B worked for all d days. So 6(d-8) + 3d + 4(d-12) = 216. Solving: 6d - 48 + 3d + 4d - 48 = 216, so 13d = 312, giving d = 24 days.

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