Multiple choice

$A$ can finish a work in $24$ days, $B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are force to leave after $3$ days. The remaining work was done by $A$ in:

  1. $5$ days
  2. $6$ days
  3. $10$ days
  4. $10\cfrac{1}{2}$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate is 1/24, B's is 1/9, C's is 1/12. B and C work for 3 days, completing 3 * (1/9 + 1/12) = 3 * (4/36 + 3/36) = 3 * (7/36) = 7/12 of the work. Remaining work is 1 - 7/12 = 5/12. A completes this in (5/12) / (1/24) = 5/12 * 24 = 10 days.

AI explanation

The combined one day work of B and C is 1/9 + 1/12, which equals 7/36. Over 3 days, B and C complete 3 x (7/36) = 7/12 of the job, leaving 5/12 of the job unfinished. Since A takes 24 days to complete a full job alone, A's daily work rate is 1/24. The time A needs to finish the remaining 5/12 of the work is (5/12) divided by (1/24), which results in 10 days.

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