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P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?

Correct answer: C. 15 days

  • A. 10 days
  • B. 14 days
  • C. 15 days
  • D. 9 days

Explanation

P's rate is 1/20 job per day, while Q and R add 1/30 + 1/60 = 1/20 job per day on every third day. In each 3-day cycle, the work is 1/20 + 1/20 + (1/20 + 1/30 + 1/60) = 1/5 job, so 5 cycles complete the job in 5 x 3 days = 15 days. The likely mistake is option a, 10 days, from assuming Q and R assist every day rather than only on every third 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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