Multiple choice

A takes 20 days to complete a piece of work. B takes 10 days to complete the same piece of work. C takes 30 days to complete the same work. A starts the work and B joins him after 5 days. C joins them 4 days later. Find the time taken by the three of them to complete the work after C joins them.

  1. 9 11 days

  2. 3 4 days

  3. 1 day

  4. 24 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/20, B's = 1/10, C's = 1/30. In 5 days, A does 5/20 = 1/4. In next 4 days, A+B do 4(1/20 + 1/10) = 4(3/20) = 12/20 = 3/5. Total done = 1/4 + 3/5 = 17/20. Remaining = 3/20. A+B+C rate = 1/20 + 2/20 + 1.33/20 = 6/60 = 1/10. Time = (3/20) / (1/10) = 1.5 days.

AI explanation

The daily work rates for A, B, and C are 1/20, 1/10, and 1/30 respectively. A works alone for 5 days, completing 5/20 or 1/4 of the job, leaving 3/4 of the job remaining. A and B then work together for 4 days at a combined rate of (1/20 + 1/10) = 3/20 per day, completing 4 * (3/20) = 3/5 of the job. The remaining work is (3/4 - 3/5) = (15/20 - 12/20) = 3/20 of the job. When C joins, their new combined rate is (1/20 + 1/10 + 1/30) = (3/60 + 6/60 + 2/60) = 11/60 per day. Dividing the remaining 3/20 (or 9/60) of the work by the combined rate of 11/60 gives 9/11 days to complete the work.

Keep practicing — related questions