Multiple choice

Ron and Sam together can do a piece of work in 8 days. Both start the work together; but after 3 days, Ron falls ill. Sam alone finishes the remaining work in 15 days. How many days would Ron take to finish the whole work alone?

  1. 10

  2. 11

  3. 12

  4. 15

  5. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ron and Sam do 1/8 of the work per day. In 3 days, they do 3/8 of the work. Remaining work = 5/8. Sam does 5/8 of the work in 15 days, so Sam's rate is (5/8)/15 = 1/24 per day. Ron's rate = (1/8) - (1/24) = 3/24 - 1/24 = 2/24 = 1/12. Ron takes 12 days to finish the work alone.

AI explanation

Assume Ron and Sam complete 1 unit of work per day together, making the total work 8 units over 8 days. In 3 days, they complete 3 units, leaving 5 units of work for Sam. Sam takes 15 days to complete these 5 units, so his daily work rate is 5 units divided by 15 days, which is 1 third of a unit per day. Their combined rate of 1 unit per day means Ron's daily rate is 1 minus 1 third, resulting in 2 thirds of a unit per day. To complete the entire 8 units of work alone, Ron requires 8 units divided by 2 thirds units per day, which totals 12 days.

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