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
Correct Answer: 4
Solution : Let the time taken by B be $x$ hour. Work done by B in 1 hr = $\frac{1}{x}$ Work done by (A + B – C) in 1 hr = $\frac{7}{30}$ According to the question: ⇒ $\frac{1}{15} + \frac{1}{x} - \frac{1}{12} = \frac{7}{30}$ ⇒ $\frac{1}{x} = \frac{7}{30} + \frac{1}{12} - \frac{1}{15}$ ⇒ $\frac{1}{x}= \frac{(14 + 5 - 4)}{60}$ ⇒ $\frac{1}{x}= \frac{15}{60}$ ⇒ $\frac{1}{x}= \frac{1}{4}$ ⇒ $x = 4$ hours Hence, the correct answer is 4.
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Question : Pipes A, B and C can fill a tank in 10, 15 and 30 hours, respectively. D is an emptying pipe which alone can empty the full tank in $x$ hours. A, B and C are opened together for 3 hours and then closed. Now D is opened which alone empties the tank in 30 hours. What is the value of $x$?
Option 1: 50
Option 2: 40
Option 3: 60
Option 4: 45
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 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 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 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: $5$
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