Two pipes A and B can fill a tank in 48 minutes and 66 minutes, respectively. If both the pipes are opened simultaneously, then after how many minutes should pipe B be closed so that the tank gets filled in 32 minutes?
22
Let the total amount of work (filling the tank) be represented by 1 unit. The rate at which pipe A fills the tank is 1/48 units per minute, and the rate at which pipe B fills the tank is 1/66 units per minute.
Let pipe B be closed after 'x' minutes. In 32 minutes, the total work done by both pipes is:
Work done by A = 32 × (1/48) = 2/3 unit.
Work done by B for 'x' minutes = x × (1/66).
The total work is 1 unit, so:
2/3 + x/66 = 1.
Solving for x, we get x = 22 minutes.
Thus, the correct answer is option 1: 22 minutes.
Similar Questions
The compound interest on Rs. 64,000 for 3 years, compounded annually at 7.5% p.a. is
The tank is filled by three pipes with different uniform flow rates. While the first two pipes are operating simultaneously, they fill the tank in the same duration that the third pipe takes to fill it alone. The second pipe can fill the tank 5 hours quicker than the first pipe, yet 4 hours slower than the third pipe. What is the time (in hours) needed for the first pipe to fill the tank?
Pipes P and Q can completely fill a water tank in 10 hours and 15 hours, respectively. A pipe R can empty a tank filled completely with water in 12 hours. Initially, the tank is empty, and only pipes P and Q are opened at 6 a.m., and pipe R is also opened at 9 a.m. By what time will the tank be completely filled?
A pipe can fill an overhead tank in 12 hours. But due to a leak at the bottom, it is filled in 18 hours. If the tank is full, how much time will the leak take to empty it?
Pipe L can fill a pool in 30 hours and pipe M in 45 hours. If both the pipes are opened in an empty pool, how much time will they take to fill it?
Three pipes P, Q, and R can fill a cistern in 40 minutes, 80 minutes, and 120 minutes, respectively. Initially, all the pipes are opened. After how much time (in minutes) should the pipes Q and R be turned off so that the cistern will be completely filled in just half an hour?
Two pipes P and Q can fill a tank in 36 minutes and 45 minutes, respectively. If both pipes are opened together, the time taken to fill the tank is:
A cistern can be filled by two pipes in 8 minutes and 10 minutes, separately. Both the pipes are opened together for a certain time, but due to an obstruction, only \( \frac{5}{8} \) of the full quantity of water flowed through the former pipe and \( \frac{3}{5} \) through the latter pipe. However, the obstruction was suddenly removed, and the cistern was filled in 3 minutes from that moment. How long did it take before the full flow began?
Pipe X can fill a tank in 9 hours and Pipe Y can fill it in 21 hours. If they are opened on alternate hours and Pipe X is opened first, in how many hours shall the tank be full?
Two pipes A and B can fill a tank in 20 and 30 hours, respectively. Both pipes are opened to fill the tank, but when the tank is one-third full, a leak develops through which one-fourth of the water supplied by both pipes goes out. Find the total time (in hours) taken to fill the tank.
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
Two pipes A and B can fill a cistern in 6 and 8 minutes respectively. If A starts the work and they be turned on alternatively for one minute each, how long will it take to fill the cistern?
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?
A pipe can fill a tank in 4 hours, while a leak which is at one-fourth of the height of the tank from bottom can empty upto that part in 2 hours. If both are operated simultaneously and initially the tank is full, then when it will be one-fourth full?
