Question : Three pipes A, B, and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and, A and B fill it in 7 hours more. The time taken by C alone to fill the cistern is:
Option 1: 14 hours
Option 2: 15 hours
Option 3: 16 hours
Option 4: 17 hours
Correct Answer: 14 hours
Solution : In 1 hour (A + B + C) fills $\frac{1}{6}$ part of the tank. In 2 hours (A + B + C) fills $\frac{1}{6}$ × 2 = $\frac{1}{3}$ part of the tank. In 7 hours (A + B) fills the remaining $(1-\frac{1}{3}$) = $\frac{2}{3}$ part of the tank. In 1 hour (A + B) fills $\frac{2}{21}$ of the tank. Therefore, C's 1 hour of work = (A + B + C)'s 1-hour work – (A + B)'s 1-hour work $=\frac{1}{6}-\frac{2}{21}=\frac{1}{14}$ So, C alone can fill the tank in 14 hours. Hence, the correct answer is 14 hours.
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Question : Pipes A, B and C together can fill a cistern in 12 hours. All three pipes are opened together for 4 hours and then C is closed. A and B together take 10 hours to fill the remaining part of the cistern. C alone will fill two-thirds of the cistern in:
Option 1: 60 hours
Option 2: 40 hours
Option 3: 48 hours
Option 4: 50 hours
Question : Three pipes, A, B, and C can fill an empty cistern in 2, 3, and 6 hours respectively. They are opened together. After what time should B be closed, so that the cistern gets filled in exactly 1 hr 15 min?
Option 1: 20 min
Option 2: 45 min
Option 3: 30 min
Option 4: 15 min
Question : Pipes A, B and C can fill an empty tank in $\frac{30}{7}$ hours if all three pipes are opened simultaneously. A and B are filling pipes and C is an emptying pipe. Pipe A can fill the tank in 15 hours and pipe C can empty it in 12 hours. In how much time (in hours) can pipe B alone fill the empty tank?
Option 1: 3
Option 2: 5
Option 3: 6
Option 4: 4
Question : When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?
Option 1: 15
Option 2: 18
Option 3: 10
Option 4: 9
Question : A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Also pipe A, working alone, takes half the time taken by pipe B. Together they take 6 hours 40 minutes to empty the pool. The time taken by pipe A to empty the pool, (in hours) is:
Option 1: 15 hours
Option 2: 10 hours
Option 3: 30 hours
Option 4: 7 hours
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