Multiple choice

A, B and C can do a work in 15 days. They started the work and after 6 days, A left. B and C finished the work in another 15 days. In how much time can A alone finish the work?

  1. 32.5 days

  2. 35 days

  3. 37.5 days

  4. 42 days

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A, B, and C together complete 1/15 of the work per day. In 6 days, they complete 6/15 = 2/5 of the work, leaving 3/5 to be finished by B and C in 15 days, meaning B and C complete 1/25 of the work per day. Subtracting (B+C)'s rate from (A+B+C)'s rate gives A's rate: 1/15 - 1/25 = (5-3)/75 = 2/75. Thus, A takes 75/2 = 37.5 days to finish the work alone.

AI explanation

Let the total work be the least common multiple of 15 and 15, which is 15 units. The combined efficiency of A, B, and C is 15 divided by 15, equaling 1 unit per day. In 6 days, they complete 6 units, leaving 9 units of work. B and C finish these 9 units in 15 days, making their combined efficiency 9 divided by 15, or 3/5 units per day. A's efficiency is 1 minus 3/5, which is 2/5 units per day. Therefore, A alone needs 15 divided by 2/5 days, resulting in 37.5 days.

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