Multiple choice

A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. A alone can do the work in

  1. 15 days

  2. 24 days

  3. 30 days

  4. 40 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B=1/12, B+C=1/15, C+A=1/20. Sum: 2(A+B+C) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5. So A+B+C = 1/10. A = (A+B+C) - (B+C) = 1/10 - 1/15 = (3-2)/30 = 1/30. A takes 30 days.

AI explanation

Using the combined work formula, the work rates of the pairs are 1/12 for A and B, 1/15 for B and C, and 1/20 for C and A. Adding these three equations gives 2 times the sum of the daily work rates of A, B, and C equal to 1/12 plus 1/15 plus 1/20, which simplifies to 1/5. Dividing by 2 gives their combined daily work rate as 1/10. To find A's individual rate, subtract the combined rate of B and C (1/15) from the total rate (1/10), resulting in 1/30, which means A alone takes 30 days.

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