Question : There are two inlets A and B connected to a tank. A and B can fill the tank in 32 h and 28 h, respectively. If both the pipes are opened alternately for 1 h, starting with A, then in how much time (in hours, to the nearest integer) will the tank be filled?
Option 1: 22
Option 2: 30
Option 3: 36
Option 4: 24
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Correct Answer: 30
Solution : Given, Pipe A can fill the tank in 32 hours ⇒ Part of the tank filled by pipe A in 1 hour = $\frac{1}{32}$ Pipe B can fill a tank in 28 hours ⇒ Part of the tank filled by B in 1 hour = $\frac{1}{28}$ The part filled by (A + B) in 2 hours = $\frac{1}{32} + \frac{1}{28}=\frac{7+8}{224}=\frac{15}{224}$ Now, $14 × \frac{15}{224} = \frac{210}{224}$ ⇒ In 14 × 2 = 28 hours tank filled by $\frac{210}{224}$ part. ⇒ Remaining = $1 - \frac{210}{224}=\frac{224-210}{224}=\frac{14}{224}$ part After completion of 28 hours pipe A will be open To fill $\frac{1}{32}$ part pipe A takes time 1 hour Remaining for 30th hours = $\frac{14}{224}-\frac{1}{32} = \frac{7}{224}$ ⇒ To fill $\frac{7}{224}$ part pipe B will take time ⇒ $\frac{7}{224}\times28$ $\approx$ 1 hours ⇒ Total time taken to fill the tank = (28 + 1 + 1) hours = 30 hours Hence, the correct answer is 30 hours.
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Question : An inlet pipe can fill an empty tank in $4 \frac{1}{2}$ hours, while an outlet pipe drains a filled tank in $7 \frac{1}{5}$ hours. The tank is initially empty, and the two pipes are alternately opened for an hour each, till the tank is filled, starting with the inlet pipe. In how many hours will the tank be filled?
Option 1: 24 hours
Option 2: $20 \frac{1}{4}$ hours
Option 3: $20 \frac{3}{4}$ hours
Option 4: $22 \frac{3}{8}$ hours
Question : Two pipes, S1 and S2, can alone fill an empty tank in 15 hours and 20 hours, respectively. Pipe S3 alone can empty that filled tank in 40 hours. Firstly, both pipes, S1 and S2, are opened and after 2 hours, pipe S3 is also opened. In how much time will the tank be filled after S3 is opened?
Option 1: $\frac{90}{17}\ \text{hours}$
Option 2: $\frac{89}{12}\ \text{hours}$
Option 3: $\frac{90}{13}\ \text{hours}$
Option 4: $\frac{92}{11}\ \text{hours}$
Question : Pipes A, B and C can fill a tank in 20, 30 and 60 hours, respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 9 a.m., respectively, on the same day. When will the tank be full?
Option 1: 4:40 p.m.
Option 2: 5:40 p.m.
Option 3: 6:20 p.m.
Option 4: 7:20 p.m.
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 : 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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