Two taps can fill a tub in 5 min and 7 min. A pipe can empty it in 3 min. When will the tub be completely full if all the three are kept open simultaneously?

Using the least common multiple method, let the total capacity of the tub be 105 liters. The two filling taps work at rates of 21 and 15 liters per minute, while the emptying pipe works at 35 liters per minute. The net filling rate when all three are open is 21 plus 15 minus 35, which equals 1 liter per minute. Dividing the total capacity of 105 liters by this net rate gives 105 divided by 1, resulting in 105 minutes. The answer is 105 min.

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