P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in__________?
Correct answer: B. 25 days
- A. 30 days
- B. 25 days
- C. 20 days
- D. 15 days
Explanation
Let Q's rate be q and R's rate be 1/50. Since P can do the work in the same time as Q and R together, P's rate is q + 1/50. Also P+Q has rate 1/10, so 2q + 1/50 = 1/10, giving q = 1/25 and a time of 25 days. The likely mistake is 30 days, which can result from ignoring that P's rate already includes Q's and R's combined rate.
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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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