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A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. A alone can do the work in__________?

Correct answer: B. 30 days

  • A. 20 days
  • B. 30 days
  • C. 40 days
  • D. none of these

Explanation

The pair rates are A+B = 1/12, B+C = 1/15, and C+A = 1/20. Adding them gives 2(A+B+C) = 1/12 + 1/15 + 1/20 = 1/5, so the total rate is 1/10; A's rate is 1/10 - 1/15 = 1/30. Therefore A alone needs 30 days. The likely mistake is 20 days, which confuses the time of a pair with the time of A alone.

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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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