To solve this problem, we need to determine how the pipes A, B, and C affect the time taken to fill or empty the tank. Let's analyze the contributions of each pipe step-by-step.
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Pipes A and B are filling pipes, while pipe C is an emptying pipe. We'll initially consider the rates for filling the tank:
- Pipe A can fill the tank in 4 hours. Thus, the rate of pipe A is \frac{1}{4} of the tank per hour.
- Pipe B can fill the tank in 6 hours and 40 minutes, which is 6 + \frac{40}{60} = \frac{20}{3} hours. Therefore, the rate of pipe B is \frac{3}{20} of the tank per hour.
- Pipe C can empty the full tank in 1 hour 40 minutes, which is 1 + \frac{40}{60} = \frac{5}{3} hours. So, the rate of pipe C is -\frac{3}{5} of the tank per hour.
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Calculate the total amount filled by pipes A and B before pipe C starts emptying the tank:
- Pipes A and B start at 2:00 p.m. and 3:00 p.m., respectively, while pipe C is opened at 4:00 p.m.
- Thus, for the first hour (from 2:00 p.m. to 3:00 p.m.), only pipe A is filling the tank: \frac{1}{4} tank.
- In the next hour (from 3:00 p.m. to 4:00 p.m.), both pipes A and B are operating. Together they fill: \frac{1}{4} + \frac{3}{20} = \frac{5}{20} + \frac{3}{20} = \frac{8}{20} = \frac{2}{5} of the tank.
- Thus, by 4:00 p.m., the amount of the tank filled is \frac{1}{4} + \frac{2}{5} = \frac{5}{20} + \frac{8}{20} = \frac{13}{20}.
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Examine the situation after 4:00 p.m. when all three pipes are open:
- The combined rate of pipes A, B, and C after 4:00 p.m. is: \frac{1}{4} + \frac{3}{20} - \frac{3}{5} = \frac{5}{20} + \frac{3}{20} - \frac{12}{20} = -\frac{4}{20} = -\frac{1}{5} tank per hour.
- The tank is emptying at a rate of \frac{1}{5} tank per hour.
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Determine how long it takes to empty the filled part of the tank:
- At 4:00 p.m., \frac{13}{20} of the tank is filled. To completely empty it at a rate of \frac{1}{5} tank per hour, the time taken is:
- \frac{13}{20} \div \frac{1}{5} = \frac{13}{20} \times 5 = \frac{65}{20} = 3.25 hours.
- Thus, the tank will be empty 3.25 hours after 4:00 p.m., which is by 7:15 p.m.
Therefore, the correct answer is 7:15 p.m..
Similar Questions
Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C alone can empty the full tank in $x$ hours. When all the 3 pipes are opened together, the tank is full in $20\frac{4}{7}$ hours. What is the value of $x$?
- A tank is normally filled in 18 hours by a pipe, but it takes 6 hours more to fill the tank due to a leakage at its bottom. The leakage point can empty the tank when it is two-third full in ______ hours.
- There are three inlet pipes X, Y and Z in a tank. X and Y can fill the tank in 45 hours. Y and Z can fill the tank in 36 hours. Z and X can fill the tank in 72 hours. The number of hours in which all the three pipes can fill the tank, if operated simultaneously, is:
Pipes A and B can fill a tank in 18 hours and 27 hours, respectively, whereas pipe C can empty the full tank in 54 hours. All three pipes are opened together, but pipe C is closed after 12 hours. In how much time (in minutes) will the one-third of the remaining part of the tank be filled by A and B together?
- A tap can fill a tank in 6 hours. After 4 hours it was found that only 60% of the tank is full due to a leakage at the bottom which was then immediately repaired. In how much time will the tank be completely filled?
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?
