Pipe A can fill an empty tank in 12 hours and pipe B can empty the same full tank in 10 hours. If pipe A is kept half open and pipe B is kept one-third open, then in how many hours does the empty tank get filled while pipes A and B are working simultaneously?

Three taps A, B, and C can fill an empty tank in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three taps are opened. Taps A, B, and C release chemical solutions P, Q, and R respectively. What is the proportion of solution R in the tank after 3 minutes?

Two inlet pipes J and T can fill a tank in 120 minutes and 144 minutes respectively. If an outlet pipe Z is opened along with them, all three pipes together fill the tank in 240 minutes. How long will pipe Z alone take to empty the full tank?