Faucet A basically used as inlet pipe and Faucet B is used as outlet pipe. Faucet A and B both are opened simultaneously, all the time. When Faucet A fills the tank and Faucet B empty the tank, it will take thrice the time than when both the pipes fill the tank. When Faucet B is used for filling the tank, its efficiency remains constant. What is the ratio of efficiency of Faucet A and Faucet B respectively?

Let the individual rates of faucets A and B be a and b units per hour. When both fill the tank, their combined rate is a plus b, but when A fills and B empties, the net rate is a minus b, which takes thrice the time, making the rate one-third of their combined rate. This establishes the equation a minus b equals the quantity a plus b divided by 3. Solving this yields 3a minus 3b equals a plus b, which simplifies to 2a equals 4b, meaning the ratio of efficiency of faucet A to faucet B is 2 to 1.

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