Question : Pipes P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all three are opened at 7 AM at what time will one-fourth of the tank be filled?
Option 1: 10 AM
Option 2: 10 PM
Option 3: 11 PM
Option 4: 11 AM
Correct Answer: 10 PM
Solution : Pipe P's hourly work = $\frac{1}{10}$ unit Pipe Q's hourly work = $\frac{1}{12}$ unit Pipe C's hourly work = $-\frac{1}{6}$ unit When all pipes are working together, let the tank be filled in $x$ hours. According to the question, $\frac{1}{10}+\frac{1}{12}-\frac{1}{6}=\frac{1}{x}$ $⇒\frac{1}{x}=\frac{6+5-10}{60}$ $⇒\frac{1}{x}=\frac{1}{60}$ $\therefore x =60$ Thus, $\frac{1}{4}$th of the tank is filled in $\frac{1}{4}×60 = 15$ hours At 7:00 AM, all pipes start working, so the required time is (7:00 AM + 15 hours) = 10:00 PM Hence, the correct answer is 10 PM.
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Question : Pipes A and B can fill an empty tank in 6 and 8 hours respectively, while pipe C can empty the full tank in 10 hours. If all three pipes are opened together, then the tank will get filled in:
Option 1: $4 \frac{4}{23}$ hours
Option 2: $6\frac{1}{5}$ hours
Option 3: $5\frac{5}{23}$ hours
Option 4: $7\frac{1}{2}$ hours
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 : Two pipes, A and B, can fill a tank in 15 hours and 18 hours, respectively. Both pipes are opened simultaneously to fill the tank. In how many hours will the empty tank be filled?
Option 1: $8 \frac{2}{11}$
Option 2: $9 \frac{2}{11}$
Option 3: $7 \frac{2}{11}$
Option 4: $10 \frac{2}{11}$
Question : Two pipes A and B can fill a tank in 12 hours and 18 hours, respectively. Both pipes are opened simultaneously. In how much time will the empty tank be filled completely?
Option 1: 9 hours 30 minutes
Option 2: 8 hours
Option 3: 7 hours 12 minutes
Option 4: 10 hours 24 minutes
Question : Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all three pipes are opened simultaneously?
Option 1: $\frac{50}{7}$
Option 2: $\frac{15}{7}$
Option 3: $\frac{30}{7}$
Option 4: $\frac{20}{7}$
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