A tank can be filled by Pipe A in 9 hours and by Pipe B in 12 hours. Pipe C can empty the tank in 18 hours. All three pipes are opened simultaneously, but Pipe C is closed after 4 hours. How much total time in all will it take to fill the tank completely?
$\frac{44}{7}$ hours
To solve the problem, we need to determine how long it takes to fill the tank when all three pipes are used but Pipe C is closed after 4 hours. Let's break it down step-by-step:
Step 1: Determine individual rates of the pipes.
- Pipe A fills the tank in 9 hours, so it fills \frac{1}{9} of the tank in one hour.
- Pipe B fills the tank in 12 hours, so it fills \frac{1}{12} of the tank in one hour.
- Pipe C empties the tank in 18 hours, so it empties \frac{1}{18} of the tank in one hour.
Step 2: Calculate the net rate of the three pipes working together for the first 4 hours.
- The combined rate of Pipes A, B, and C is:
- \frac{1}{9} + \frac{1}{12} - \frac{1}{18}
To compute this, we find a common denominator:
- LCM of 9, 12, and 18 is 36.
- Convert each fraction:
- \frac{1}{9} = \frac{4}{36}, \frac{1}{12} = \frac{3}{36}, \frac{1}{18} = \frac{2}{36}
- Adding these gives: \frac{4}{36} + \frac{3}{36} - \frac{2}{36} = \frac{5}{36}
Therefore, in 1 hour, the three pipes together fill \frac{5}{36} of the tank.
Step 3: Calculate the amount of tank filled in the first 4 hours.
- In 4 hours, they will fill: 4 \times \frac{5}{36} = \frac{20}{36} = \frac{5}{9} of the tank.
Step 4: Calculate the remaining part of the tank to be filled and time required.
- The part of the tank remaining after 4 hours: 1 - \frac{5}{9} = \frac{4}{9}
- Only Pipes A and B are available now, so their combined rate is:
- \frac{1}{9} + \frac{1}{12} = \frac{4}{36} + \frac{3}{36} = \frac{7}{36} per hour.
- Time required to fill the remaining \frac{4}{9} of the tank:
- Time = \frac{\frac{4}{9}}{\frac{7}{36}} = \frac{4}{9} \times \frac{36}{7} = \frac{16}{7} hours.
Step 5: Calculate total time to fill the tank completely.
- Total time = 4 hours (initial) + \frac{16}{7} hours (remaining).
- Total time = 4 + \frac{16}{7} = \frac{28}{7} + \frac{16}{7} = \frac{44}{7} hours.
Therefore, the total time taken to fill the tank completely is \frac{44}{7} hours. Thus, the correct answer is \frac{44}{7} hours.
Similar Questions
One pipe can fill a tank in 6 minutes, while another pipe can empty the completely filled tank in 9 minutes. If both the pipes are opened together when the tank is empty, how many minutes will it take to fill one-half of the tank?
P and Q together can fill a cistern with water in 15 hours. If P alone can fill the cistern with water in 60 hours, then in how many hours will Q alone fill one-fourth of the same cistern with water?
Walking at $\frac{5}{8}$ of his normal speed from his home, Tarun is 21 minutes late. The usual time taken by him to cover the distance between his home and office is:
A contractor agreed to complete a job in 74 days. He employed 21 men to work, but only one-fourth of the work was completed in 32 days. How many additional men must he employ to finish the remaining work within the stipulated time?
A tap can fill a cistern in 10 hours and another tap can empty it in 20 hours. If both taps are opened, the time (in hours) taken to fill the tank will be:
A, B and C can do a piece of work in 2, 15 and 10 days, respectively. How long (in days) will they take to do twice the same work, working together?
Pipe A can fill a tank in 6 hours, pipe B can fill the same tank in 36 hours and pipe C can fill the same tank in 18 hours. The time taken (in hours) by them to fill one-fourth of the same tank if they operate together is:
Pipe A can fill a tank in 4 hours, pipe B can fill the same tank in 6 hours and pipe C can fill the same tank in 12 hours. The time taken (in hours) by them to fill half of the same tank if they operate together is:
Pipe A can fill a tank in 6 hours, pipe B can fill the same tank in 28 hours and pipe C can fill the same tank in 21 hours. The time taken (in hours) by them to fill one-fourth of the same tank if they operate together is:
Pipe A can fill a tank in 6 hours, pipe B can fill the same tank in 21 hours and pipe C can fill the same tank in 28 hours. The time taken (in hours) by them to fill one-fourth of the same tank if they operate together is:
Important Questions from Pipe and Cistern
Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely?
The compound interest on Rs. 64,000 for 3 years, compounded annually at 7.5% p.a. is
A water tank can be emptied in 40 minutes by a pipe of d 'diameter, so how long will it take for a 2d diameter pipe to be emptied?
Two pipes X and Y can fill an empty tank in 16 hours and 20 hours respectively. Pipe Z alone can empty the completely filled tank in 25 hours. Firstly both pipes X and Y are opened and after 6 hours pipe Z is also opened. What will be the total time (in hours) taken to completely fill the tank?
Pipe J can fill a tank in 48 hours and pipe K can fill the same tank in 72 hours. If both the pipes are opened alternately for one hour each and pipe K is opened for the first hour, then in how much time the tank will be full?
