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: $15\frac{1}{2}$
Correct Answer: $12 \frac{1}{2}$
Solution : Pipe A can fill in 1 hour = $\frac{1}{16}$ Pipe B can fill in 1 hour = $\frac{1}{24}$ Pipe C can empty in 1 hour = $\frac{1}{40}$ Together they can fill in 1 hour $=\frac{1}{16} + \frac{1}{24} – \frac{1}{40}=\frac{19}{240}$ Together they can fill in 10 hours = $10\times\frac{19}{240}=\frac{19}{24}$ $\therefore$ Remaining tank = $1-\frac{19}{24}=\frac{5}{24}$ B and C can do in 1 hours = $\frac{1}{24} – \frac{1}{40}=\frac{2}{120}=\frac{1}{60}$ B and C can fill a tank in 60 hours. $\therefore$ B and C can fill $\frac{5}{24}$th tank = $60 × \frac{5}{24}=\frac{25}{2}=12\frac{1}{2}$ hours Hence, the correct answer is $12\frac{1}{2}$ 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 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 and B can fill a tank in 36 hours and 48 hours, respectively. Both pipes are opened together for 9 hours and then A is closed. Pipe B alone will fill the remaining part of the tank now in:
Option 1: $20 \frac{1}{2}$ hours
Option 2: $25$ hours
Option 3: $27$ hours
Option 4: $24$ hours
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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