Question : Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 8
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Correct Answer: 10
Solution : LCM of 12, 24 and 32 is 96 The capacity of the tank = 96 unit Efficiency of pipe A = $\frac{96}{12}$ = 8 unit/min Efficiency of pipe B = $\frac{96}{24}$ = 4 unit/min Efficiency of pipe C = $\frac{96}{32}$ = – 3 unit/min Combined efficiency of A + B + C = 9 unit/min Let if C is not closed 2 minutes before then Work done by C in 2 minutes = 2 × – 3 = – 6 unit Total work done by all pipes = 96 + (– 6) = 90 unit Required time = $\frac{\text{total work}}{\text{total efficiency }}$ Required time = $\frac{90}{9}$ = 10 minutes Hence, the correct answer is 10.
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Question : Pipes A and B can fill a tank in 12 minutes and 15 minutes, respectively. The tank when full can be emptied by pipe C in $x$ minutes. When all three pipes are opened simultaneously, the tank is full in 10 minutes. The value of $x$ is:
Option 1: 18
Option 2: 15
Option 3: 20
Option 4: 24
Question : An inlet pipe can fill an empty tank in 140 hours, while an outlet pipe drains a filled tank in 63 hours. If 8 inlet pipes and y outlet pipes are opened simultaneously, when the tank is empty, then the tank gets filled in 105 hours. Find the value of y.
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3
Question : Pipe A can fill an empty tank in 18 hours and Pipe B can fill the same empty tank in 24 hours. If both the pipes are opened simultaneously, how much time (in hours) will it take to fill the empty tank?
Option 1: $11 \frac{3}{7}$
Option 2: $10 \frac{1}{7}$
Option 3: $10 \frac{2}{7}$
Option 4: $11 \frac{2}{7}$
Question : Pipe A can fill 50% of the tank in 6 hours and Pipe B can fill the same tank in 18 hours. If both the pipes are opened simultaneously, how much time (in minutes) will the empty tank be filled?
Option 1: 420
Option 2: 425
Option 3: 432
Option 4: 435
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