Multiple choice

A and B can do a piece of work in 15 days. B and C together can do it in 24 days. After A worked for 5 days and B worked for 13 days, C took up and finished it in 28 days. In how many days can each of them do the work, working alone?

  1. 24, 40, 60

  2. 28, 32, 68

  3. 183/7, 54, 24

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let work rates be A, B, C. A+B = 1/15, B+C = 1/24. 5A + 13B + 28C = 1. Using A = 1/15 - B and C = 1/24 - B: 5(1/15 - B) + 13B + 28(1/24 - B) = 1. Solving for B gives B = 1/40. Then A = 1/24 and C = 1/60. Days are 24, 40, 60.

AI explanation

Let the total work be 120 units, making the efficiencies of A and B together 8 units per day, and B and C together 5 units per day. The equation for their individual work periods is 5A plus 13B plus 28C equals 120. Substituting A equals 8 minus B gives 40 minus 5B plus 13B plus 28C equals 120, simplifying to 8B plus 28C equals 80. Substituting B equals 5 minus C gives 40 minus 8C plus 28C equals 80, which means C takes 40 days alone. This results in B taking 40 days and A taking 24 days.

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