A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days. In what time can A alone do it ?
Correct answer: C. 120 days
- A. 80 days
- B. 100 days
- C. 120 days
- D. 150 days
Explanation
Using pair rates, A's rate is (AB + AC - BC)/2 = (1/72 + 1/90 - 1/120)/2 = (1/60)/2 = 1/120 work per day. Therefore A alone takes 120 days. The likely trap is 100 days, caused by combining the pair times directly instead of combining 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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