Multiple choice

A can do a piece of work in $20$ days B in $15$ days and C in $12$ days. How soon can the work be done if A is assisted by B on one day and by C on the next alternately?

  1. $14$ days
  2. $6$ days
  3. $8$ days
  4. $10$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate is 1/20, B's is 1/15, and C's is 1/12. On day 1, A and B work together (1/20 + 1/15 = 7/60); on day 2, A and C work together (1/20 + 1/12 = 8/60). In 2 days, they complete 15/60 = 1/4 of the work, so the total work takes 8 days.

AI explanation

Taking the total work as the least common multiple of 20, 15 and 12, the work is 60 units. The daily capacities of A, B and C are 3, 4 and 5 units respectively. In the first cycle of two days, A and B work the first day to complete 7 units, and A and C work the second day to complete 8 units, finishing 15 units every two days. After 3 such cycles spanning 6 days, 45 units are completed, leaving 15 units. On the 7th day A and B complete 7 units, leaving 8 units, which A and C complete on the 8th day.

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