A can do a certain work-in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in_________?
Correct answer: C. 25 days
- A. 15 days
- B. 20 days
- C. 25 days
- D. 30 days
Explanation
The condition says A's rate equals B plus C's rate. Since A and B together work at 1/10 work per day and C works at 1/50 work per day, 1/10 = 2B + 1/50, so B's rate is (1/10 - 1/50) ÷ 2 = 1/25 work per day. Hence B alone takes 25 days; the likely trap is 20 days, from failing to divide the remaining rate by 2.
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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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