Multiple choice

A contractor has two teams of workers, team A and team B. Team A can complete a project P in 12 days and team B can complete it in 36 days. Team A starts working on P and team B joins team A after four days. Team A is withdrawn after another two days and team B is asked to double its efficiency. The number of additional days required for team B to complete P is

  1. 6

  2. 8

  3. 15

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Team A rate = 1/12, Team B rate = 1/36. In 4 days, A does 4/12 = 1/3. In next 2 days, A+B do 2(1/12 + 1/36) = 2(4/36) = 2/9. Total done = 1/3 + 2/9 = 5/9. Remaining = 4/9. B's new rate = 2/36 = 1/18. Time = (4/9) / (1/18) = 8 days.

AI explanation

Let total work be the LCM of 12 and 36, which is 36 units, making team A's capacity 3 units per day and team B's capacity 1 unit per day. Team A works alone for 4 days to finish 12 units, then both teams work for 2 days to finish 8 units, leaving 16 units of work remaining. Because team B doubles its efficiency to 2 units per day, the additional days required are 16 divided by 2, resulting in 8 days.

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