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

It will take 12 hours to fill the tank

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 (1)/(4)+(1)/(3)-(1)/(2)=\displaystyle (3)/(12)+(4)/(12)-(6)/(12)=(3+4-6)/(12)=(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