Question : A pipe can fill a tank in 30 hours. Due to a leakage at the bottom, it is filled in 50 hours. How much time will the leakage take to empty the filled tank?
Option 1: 60 hours
Option 2: 85 hours
Option 3: 70 hours
Option 4: 75 hours
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Correct Answer: 75 hours
Solution : The pipe fills the tank in 30 hours. So, it fills $\frac{1}{30}$th of the tank in 1 hour. With the leak, the pipe fills $\frac{1}{50}$th the tank in 1 hour. The volume the leak empties in 1 hour $=\frac{1}{30} - \frac{1}{50} = \frac{5 - 3}{150} = \frac{2}{150} = \frac{1}{75}$ So, the leak will empty the full tank in 75 hours. Hence, the correct answer is 75 hours.
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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
Question : Pipe A can fill an empty tank in 6 hours and pipe B, in 8 hours. If both pipes are opened and after 2 hours, pipe A is closed, how much time will B take to fill the remaining tank?
Option 1: $7\frac{1}{2}$ hours
Option 2: $2\frac{2}{5}$ hours
Option 3: $2\frac{1}{3}$ hours
Option 4: $3\frac{1}{3}$ hours
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 : 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
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