Pipes and Cistern Questions

• Two pipes fill a reservoir. Working simultaneously, they fill it in 12 hours. One pipe is 10 hours faster than the other (i.e., it takes 10 fewer hours to fill the reservoir alone). How many hours does the faster pipe take to fill the reservoir alone?
• Pipes A and B can fill a tank in 15 hours and 20 hours, respectively, while Pipe C can empty a full tank in 25 hours. All three pipes are opened together. After 10 hours, Pipe C is closed and A and B continue. What is the total time (from the start) required to fill the tank completely?
• A cistern that would normally be filled by an inlet in 9 hours takes 1 hour longer to be filled because of a leak at the bottom. If the cistern is full, in how many hours would the leak alone empty it?
• A cistern has three pipes: Inlet A fills it in 2 hours, Inlet B fills it in 3 hours, and Pipe C is a waste (outlet). When all three are opened together, 7/24 of the cistern is filled in 30 minutes. How long does C alone take to empty a full cistern?
• Two inlets P and Q can fill a cistern in 12 minutes and 15 minutes, respectively. Both are opened together, but after exactly 3 minutes, P is turned off and only Q continues. How much longer (beyond the first 3 minutes) will it take to fill the cistern completely?
• Three inlets A, B, and C can fill a cistern in 10 hours, 12 hours, and 15 hours, respectively. First, A alone is opened. After 1 hour from the start, B is also opened. After 2 hours from the start (i.e., 1 more hour later), C is also opened. From the start of A, in what total time will the cistern be just full?
• Two inlets fill a cistern in 12 minutes and 15 minutes, respectively, and a third pipe can empty a full cistern in 6 minutes. The first two pipes are kept open for 5 minutes; then the third pipe is also opened along with them. From the instant the third pipe is opened, in what time is the cistern emptied (reduced from its then level to empty)?
• A leak at the bottom of a tank can empty a full tank in 6 hours. An inlet supplies water at 4 litres per minute. When the tank is full, the inlet is opened; due to the leak, the tank becomes empty in 8 hours. What is the capacity of the tank (in litres)?
• Two pipes X and Y can fill a cistern in 24 minutes and 32 minutes, respectively. Both are opened together. After how many minutes should Y be closed so that the tank gets exactly full in a total of 18 minutes?
• A water tank is initially 2/5 full. Pipe A can fill the entire tank in 10 minutes, while Pipe B can empty a full tank in 6 minutes. If both pipes are opened together from this initial state, how long will it take to reach an empty or full condition? State which occurs.
• Tap A fills a tank in 25 minutes, Tap B fills it in 40 minutes, and Tap C empties it in 30 minutes. If all three taps are opened together on an empty tank, will the tank be filled or emptied, and in how many minutes?
• Two inlets A and B can fill a cistern in 12 minutes and 14 minutes, respectively, while an outlet C can empty it in 8 minutes. If all three taps are opened simultaneously on an empty cistern, what fraction of the cistern remains unfilled at the end of 7 minutes?
• Two pipes can fill a cistern in 30 minutes and 40 minutes, respectively. Both pipes are opened together, but after some time the first pipe is shut off. The cistern is filled in 10 minutes more (by the second pipe alone after the shutdown). How long after the start was the first pipe shut off?
• A cistern has a leak that would empty it in 15 hours. A tap is turned on that admits water at 2 litres per hour into the cistern. With the leak and the inlet both open, the cistern now empties in 30 hours. What is the capacity of the cistern (in litres)?
• Pipes and Cisterns – Two inlet taps with different efficiencies: Two taps A and B are used to fill the same water tank. When both taps are opened together, the tank fills in 40 minutes. If only tap A is opened, it fills the tank in 60 minutes. Determine the time required for tap B alone to fill the tank.
• Pipes and Cisterns – Two inlets and one outlet acting together: An empty cistern can be filled by tap 1 in 3 hours and by tap 2 in 4 hours, while tap 3 can empty a full cistern in 5 hours. If all three taps are opened at the same time starting from empty, in how much time will the cistern become full?
• Pipes and Cisterns – Two inlets and one outlet together from empty: Pipe A fills the tank in 30 minutes, pipe B fills it in 10 minutes, and pipe C empties a full tank in 40 minutes. If all three pipes are opened simultaneously starting with an empty tank, how long will it take to fill the tank completely?
• Pipes and Cisterns – Inlet with a leak delaying completion: A tank normally fills in 8 hours through a single inlet. Because of a leak at the bottom, it actually takes 10 hours to fill completely. If the tank is full, in how many hours would the leak alone empty it?
• Pipes and Cisterns – Two inlets and one outlet complete the tank in a target time: Pipe A fills the tank in 1 hour and pipe B in 75 minutes. With an outlet C also open, the tank becomes full in 50 minutes. How long would pipe C alone take to empty a full tank?
• Pipes and Cisterns – Pairwise fill times given, find time for all three together: Three pipes A, B and C are connected to a tank. A and B together fill the tank in 6 hours, B and C together in 10 hours, and A and C together in 12 hours. How long will A, B and C take to fill the tank when all three operate together from the start?