Answer:
It will take 12 hours to fill the tank
Step-by-step explanation:
Proportions
Tap A fills a tank in 4 hours. It means each hour it fills 1/4 of the tank.
Tap B fills the tank in 3 hours. Each hour it fills 1/3 of the tank.
Tap C empties the tank when full in 2 hours. Each hour it empties 1/2 of the tank.
Each hour, the tank gets filled by:
[tex]\displaystyle \frac{1}{4}+\frac{1}{3}-\frac{1}{2}=\displaystyle \frac{3}{12}+\frac{4}{12}-\frac{6}{12}=\frac{3+4-6}{12}=\frac{1}{12}[/tex]
Since the tank fills 1/12 of its capacity in one hour, it follows that it will take 12 hours to fill the tank
