Multiple choice

$A$ and $B$ can do a piece of work in $8$ days. $B$ and $C$ can do the same work in $12$ days. If $A, B$ and $C$ can complete the same work in $6$ days, in how many days can $A$ and $C$ complete the same work?

  1. $8$ days
  2. $10$ days
  3. $6$ days
  4. $2$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1/A + 1/B = 1/8, 1/B + 1/C = 1/12, 1/A + 1/B + 1/C = 1/6. (1/A + 1/B + 1/C) - (1/B + 1/C) = 1/A = 1/6 - 1/12 = 1/12. (1/A + 1/B + 1/C) - (1/A + 1/B) = 1/C = 1/6 - 1/8 = 1/24. 1/A + 1/C = 1/12 + 1/24 = 3/24 = 1/8. So A and C take 8 days.

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