Multiple choice

$A$ and $B$ can do a piece of work in 30 days. While $B$ and $C$ can do the same work in 24 days and $C$ and $A$ in 20 days. They all work together for 10 days before $B$ and $C$ leave. How many days more will $A$ take to finish the work?

  1. 18 days

  2. 24 days

  3. 30 days

  4. 36 days
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A Correct answer
Explanation

Combined rates: A+B=1/30, B+C=1/24, C+A=1/20. Summing these gives 2(A+B+C) = 1/30+1/24+1/20 = 15/120 = 1/8, so A+B+C = 1/16. In 10 days, they do 10/16 = 5/8 of the work. Remaining work is 3/8. A's rate is (A+B+C) - (B+C) = 1/16 - 1/24 = 1/48. Time for A = (3/8) / (1/48) = 18 days.

AI explanation

Using the combined work formula, 2(A+B+C) equals 1/30 + 1/24 + 1/20, which simplifies to 1/8. This makes the combined work rate of A, B, and C equal to 1/16 per day. Working together for 10 days, they complete 10/16, or 5/8 of the work, leaving 3/8 of the work remaining. Solving the system of equations, A's individual work rate is 1/60 per day. To finish the remaining 3/8 of the work at this rate, A requires (3/8) divided by (1/60) days, which equals 18 days.

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