Multiple choice

A can do a piece of work in 20 days and B can do the same piece of work in 30 days. They start working together and work for 5 days and then, both leave the work. C alone finishes the remaining work in 14 days. In how many days will C alone finish the whole work?

  1. 24

  2. 18

  3. 36

  4. 42
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/20, B's rate = 1/30. Combined rate = 1/20 + 1/30 = 5/60 = 1/12. In 5 days, they do 5/12 of the work. Remaining work = 7/12. C does 7/12 in 14 days, so C's rate = (7/12) / 14 = 1/24. C takes 24 days to finish the whole work.

AI explanation

Using the fraction of work method, A's rate is 1/20 per day and B's rate is 1/30 per day. Their combined rate is 1/20 + 1/30 = 5/60 = 1/12 per day. Working for 5 days, they complete 5/12 of the job, leaving 1 - 5/12 = 7/12 of the job. C finishes this remaining 7/12 of the job in 14 days, meaning C's daily work rate is (7/12) / 14 = 1/24. Therefore, C alone can finish the whole work in 24 days.

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