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A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in_______days.

Correct answer: A. 5 5⁄11

  • A. 5 5⁄11
  • B. 4 5⁄11
  • C. 6 4⁄11
  • D. 6 5⁄11

Explanation

A completes 12 days × 8 hours = 96 hours of work, so A's hourly rate is 1/96 work per hour; B's is 1/(8 × 10) = 1/80 work per hour. Working together for 8 hours per day, their daily rate is 8/96 + 8/80 = 11/60 work per day, giving time = 60/11 = 5 5/11 days. The likely mistake is 4 5/11 days, from combining daily rates without accounting for the stated working hours.

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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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