Question : An inlet pipe can fill an empty tank in 3.6 hours, while an outlet pipe can drain a completely filled tank in 6.3 hours. If both the pipes are opened simultaneously when the tank is empty, in how many hours will the tank get completely filled?
Option 1: 9
Option 2: 8.4
Option 3: 8.1
Option 4: 8.7
Correct Answer: 8.4
Solution : The rate at which the inlet pipe can fill the tank is 1 tank per 3.6 hours, or $\frac{1}{3.6}$ tanks per hour. The rate at which the outlet pipe can drain the tank is 1 tank per 6.3 hours, or $\frac{1}{6.3}$ tanks per hour. When both pipes are opened simultaneously, the net rate of filling the tank is the rate of the inlet pipe minus the rate of the outlet pipe. $\text{Net rate} = \frac{1}{3.6} - \frac{1}{6.3}$ ⇒ $\text{Time} = \frac{1}{\text{Net rate}}$ ⇒ $\text{Time} = \frac{1}{\frac{1}{3.6} - \frac{1}{6.3}}$ ⇒ $\text{Time} = \frac{1}{\frac{5}{18} - \frac{10}{63}}= \frac{1}{\frac{5}{42} }= \frac{42}{5}$ ⇒ $\text{Time} =8.4$ hours Hence, the correct answer is 8.4.
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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 : 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 : 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 : 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 : Two inlet pipes can fill a cistern in 10 and 12 hours respectively and an outlet pipe can empty 80 gallons of water per hour. All three pipes working together can fill the empty cistern in 20 hours. What is the capacity (in gallons) of the tank?
Option 1: 360
Option 2: 300
Option 3: 600
Option 4: 900
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