Multiple choice

A can do a piece of work in 12 days alone, B can do the same work in 16 days alone. After A has been working for 5 days and B for 7 days, C finishes it in 14 days. In how many days will C alone be able to do the work?

  1. 96

  2. 86

  3. 90

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/12, B's = 1/16. A works 5 days: 5/12. B works 7 days: 7/16. Total work done = 5/12 + 7/16 = (20+21)/48 = 41/48. Remaining work = 7/48. C finishes in 14 days, so C's rate = (7/48) / 14 = 1/96. C alone takes 96 days.

AI explanation

Let the total work be the least common multiple of 12 and 16, which is 48 units. The daily work units of A and B are 4 and 3 respectively. A works for 5 days to complete 20 units and B works for 7 days to complete 21 units, leaving 7 units for C. Since C finishes the remaining 7 units in 14 days, C's daily work is 0.5 units. Therefore, C alone would take 48 divided by 0.5, which equals 96 days.

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