Multiple choice

A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?

  1. 17 1/2 days

  2. 44 days

  3. 24 days

  4. 30 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work in 10 days = 10/40 = 1/4. B's work in 10 days = 10/30 = 1/3. Remaining work = 1 - (1/4 + 1/3) = 1 - 7/12 = 5/12. C does 5/12 of the work in 10 days, so C does the whole work in 10 * (12/5) = 24 days.

AI explanation

Using the fraction of work method, let the total work be the least common multiple of 40 and 30, which is 120 units. A's rate is 3 units per day and B's rate is 4 units per day. A and B each work for 10 days, completing 30 and 40 units respectively, totaling 70 units and leaving 50 units for C. Since C completes 50 units in 10 days, C's rate is 5 units per day, meaning C alone would take 120 divided by 5 days. The result is 24 days.

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