DIRECTION for the question: Solve the following question and mark the best possible option.

Eight pipes are fitted to a water tank. Some of these are water pipes to fill the tank and the remaining are waste pipes used to empty the tank. Each water pipe can fill the tank in 12 hours and each waste pipe can empty it in 36 hours. On opening all the pipes an empty tank is filled in 3 hours. The number of waste pipe is?

Let the number of filling pipes = f

Let the number of waste pipes = w

f + w = 8 ----(1)

Each fill pipe completely fills the empty tank in 12 hours

Each waste pipe empties the completely filled tank in 36 hours

Let total volume of tank = LCM (12, 360) = 36 units

$$\therefore$$ Efficiency of fill pipe = 36/12 = 3 units/hour

$$\therefore$$ Efficiency of waste pipe = 36/36 = 1 unit/hour

Volume of tank filled by 'f' fill pipes and 'w' waste pipes = (3f - w) units/hour

It is given that the tank gets filled in 3 hours

$$\therefore$$ 3 $$\times$$ (3f - w) = 36

$$\therefore$$ 3f - w = 12 ----(2)

Adding (1) and (2), we get,

4f = 20 $$\Rightarrow$$ f = 5

$$\therefore$$ w = 8 - f = 3

Hence, option A is the correct choice.