P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
Correct answer: B. 8
- A. 7
- B. 8
- C. 9
- D. 10
Explanation
The rates of P+Q, Q+R, and P+Q+R are 1/8, 1/12, and 1/6 work per day. Q's rate is 1/8 + 1/12 - 1/6 = 1/24, so P+R's rate is 1/6 - 1/24 = 1/8. Therefore P and R need 8 days together. The likely mistake is 9 days, which comes from combining the pair times directly 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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