X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?
Correct answer: B. 10 days
- A. 6 days
- B. 10 days
- C. 15 days
- D. 20 days
Explanation
X completes 4 x 1/20 = 1/5 of the work in the first 4 days, leaving 4/5 of the work. After Y joins, their combined rate is 1/20 + 1/12 = 2/15 work per day, so the remaining work takes (4/5) ÷ (2/15) = 6 days; the total duration is 4 + 6 = 10 days. The likely trap is 6 days, which counts only the period after Y joined.
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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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