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P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

Correct answer: D. 13

  • A. 9
  • B. 11
  • C. 23
  • D. 13

Explanation

P's rate is 1/23 work per day; since P is 30% more efficient, Q's rate is 1/1.3 of P's rate = 10/299 work per day. Together their rate is 1/23 + 10/299 = 13/299 + 10/299 = 23/299 work per day, so time = 299/23 = 13 days. The likely mistake is 23 days, which ignores Q's contribution.

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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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