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
Correct Answer: $5\frac{5}{23}$ hours
Solution : Hourly work done by A = $\frac{1}{6}$ Hourly work done by B = $\frac{1}{8}$ Hourly work done by C = $\frac{1}{10}$ The tank can be filled by A, B, and C = $\frac{1}{6}+\frac{1}{8}-\frac{1}{10}$ = $\frac{20+15-12}{120}$ = $\frac{23}{120}$ The tank can be filled in $\frac{120}{23}=5\frac{5}{23}$ hours Hence, the correct answer is $5\frac{5}{23}$ hours.
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Question : Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe C is closed after 10 hours. After how many hours will the remaining part of the tank be filled?
Option 1: $2 \frac{1}{2}$
Option 2: $2$
Option 3: $5 \frac{1}{2}$
Option 4: $5$
Question : Pipes A and B can empty a full tank in 18 hours and 24 hours, respectively. Pipe C alone can fill the tank in 36 hours. If the tank is $\frac{5}{6}$ full and all the three pipes are opened together, then in how many hours will the tank be emptied?
Option 1: $10 \frac{1}{2}$
Option 2: $12 \frac{1}{2}$
Option 3: $10$
Option 4: $12$
Question : Pipes A and B can fill a tank in 18 minutes and $22 \frac{1}{2}$ minutes, respectively while pipe C can empty the full tank in 12 minutes. A and B are opened together for 6 minutes and then closed. Now C is opened. C alone will empty the tank in ____.
Option 1: $5$ minutes
Option 2: $8 \frac{2}{5}$ minutes
Option 3: $7 \frac{1}{5}$ minutes
Option 4: $6$ 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: $\frac{20}{7}$
Question : Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe A is closed after 10 hours. After how many hours will the remaining part of the tank be filled?
Option 1: $12 \frac{1}{2}$
Option 2: $10$
Option 3: $20$
Option 4: $15\frac{1}{2}$
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