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P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in__________days.

Correct answer: A. 12

  • A. 12
  • B. 15
  • C. 22
  • D. 20

Explanation

P's rate is 1/15 job per day and Q's rate is 1/10 job per day. In 2 days they complete 2/15 + 2/10 = 1/3 of the job, leaving 2/3; P takes (2/3) / (1/15) = 10 days, so total time is 2 days + 10 days = 12 days. The likely mistake is option b, 15 days, from ignoring the work completed by Q before he left.

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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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