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
Correct Answer: 50
Solution : Let the capacity of the tank as $V$. The rates at which pipes A, B, and C fill the tank are $\frac{V}{10}$, $\frac{V}{15}$, and $\frac{V}{30}$ units per hour, respectively. The rate at which pipe D empties the tank is $\frac{V}{x}$ units per hour. In the first 3 hours, pipes A, B, and C together fill the tank with $3 \left(\frac{V}{10} + \frac{V}{15} + \frac{V}{30}\right)$ units of water. After that, pipe D alone empties the tank in 30 hours, so it empties $30 \left(\frac{V}{x}\right)$ units of water. Since the amount of water filled by pipes A, B, and C is equal to the amount of water emptied by pipe D. $⇒3 \left(\frac{V}{10} + \frac{V}{15} + \frac{V}{30}\right) = 30 \left(\frac{V}{x}\right)$ $⇒ \left(\frac{1}{10} + \frac{1}{15} + \frac{1}{30}\right) = 10 \left(\frac{1}{x}\right)$ $⇒ \frac{1}{5} = 10 \left(\frac{1}{x}\right)$ $⇒x=50$ Hence, the correct answer is 50.
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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 : 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 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: $15\frac{1}{2}$
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 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
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