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A can do piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?

Correct answer: B. 120/7 days

  • A. 70 days
  • B. 120/7 days
  • C. 50 days
  • D. 45 days

Explanation

A's rate is 1/30 work per day and B's rate is 1/40 work per day, so together their rate is 1/30 + 1/40 = 7/120 work per day. Therefore, time = 1 ÷ (7/120) = 120/7 days. The likely trap is 70 days, from adding the individual times instead of their rates.

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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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