Multiple choice

A can complete a work in 20 days and B can do the same in 30 days. A works alone for 4 days and then B completes the remaining work along with C in 18 days. In how many day can C complete the work alone?

  1. 72

  2. 90

  3. 12

  4. 68
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate is 1/20, B's is 1/30. A works for 4 days, doing 4/20 = 1/5 of the work. Remaining work is 4/5. B and C complete this in 18 days, so (1/30 + C) * 18 = 4/5. Solving for C: 1/30 + C = 4/90 = 2/45. C = 2/45 - 1/30 = 4/90 - 3/90 = 1/90. Thus, C takes 90 days.

AI explanation

Let the total work be the least common multiple of 20 and 30, which is 60 units, meaning A's efficiency is 3 units per day and B's efficiency is 2 units per day. A works alone for 4 days, completing 4 times 3 equaling 12 units, leaving 48 units of work. B and C complete the remaining 48 units in 18 days, so their combined daily efficiency is 48 divided by 18, equaling 8 over 3 units. Since B works at 2 units per day, C's daily efficiency is 8 over 3 minus 2, equaling 2 over 3 units per day. Dividing the total work of 60 units by C's efficiency of 2 over 3 gives 90 days for C to complete the work alone.

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