Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
Correct answer: C. 8 1/4 min
- A. 3 1/4 min
- B. 5 1/4 min
- C. 8 1/4 min
- D. 9 1/4 min
Explanation
In the first 3 minutes, A and B fill 3 x (1/12 + 1/15) = 3 x 3/20 = 9/20 of the cistern. The remaining 11/20 is filled by B alone at 1/15 cistern per minute, so the additional time is (11/20) ÷ (1/15) = 33/4 = 8 1/4 minutes. A student may choose 5 1/4 minutes by subtracting the first 3 minutes from the total incorrectly.
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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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