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C takes 6 days to complete half of a work and D takes 5 days to complete 1/3rd of the same work. They take turns to complete the task. If C works for the first 4 days, in how many days will D complete the rest of the work without the help of C?

Correct answer: A. 10 days

  • A. 10 days
  • B. 12 days
  • C. 8 days
  • D. 9 days

Explanation

C completes half the work in 6 days, so C's rate is 1/12 of the work per day; in 4 days C completes 4/12 = 1/3 of the work, leaving 2/3. D completes 1/3 in 5 days, so D's rate is 1/15 of the work per day, and the remaining work takes (2/3) ÷ (1/15 per day) = 10 days. Students may choose 12 days by treating D's rate as 1/18 of the work per day.

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About Time and Work

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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