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A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately. If A begins first, in how many days the work will be completed ?

Correct answer: B. 41/4 days

  • A. 42/4 days
  • B. 41/4 days
  • C. 55 days
  • D. None of these

Explanation

In each two-day cycle, A and B complete 1/9 + 1/12 = 7/36 of the work. After four cycles, 28/36 = 7/9 is complete; A then works on day 9, B on day 10, and the remaining 1/36 is completed by A in (1/36) ÷ (1/9) = 1/4 day, giving 10 1/4 = 41/4 days. The likely mistake is 42/4 days, caused by rounding the final quarter-day or mishandling the alternating sequence.

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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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