Question

Tap A fills a tank in 4hours while B fills the same tank in 3hours. Tap C empties this tank when full in 2hours. If the tank is initially empty and all three taps are opened, how long will it take to fill the tank?

Answer 1

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:

$\displaystyle \frac{1}{4}+\frac{1}{3}-\frac{1}{2}=\displaystyle \frac{3}{12}+\frac{4}{12}-\frac{6}{12}=\frac{3+4-6}{12}=\frac{1}{12}$

Since the tank fills 1/12 of its capacity in one hour, it follows that it will take 12 hours to fill the tank