Question

There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes​

Answer 1

Answer:

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Step-by-step explanation:

Let fill pipes be "X"

Drain pipes = 12-n

All the fill pipes together can fill tank in 8 hrs

So, one fill pipe can fill it for 1/8 hrs

Hence x fill pipes can fill it in x/8 hrs

Each drain pipe will drain the tank in 6 hrs

Therefore , each of the drain pipe will drain pipes will drain (1/6) hrs

Drain pipes = 12-x

Hence all drain pipes can drain it in 12-x/6 hrs

When all these 12 pipes are kept open, it takes 24 hrs for an empty tank to over flow.

In an hour 1/24 of the tank gets filled.

Hence,

(x/8)-(12-x/6) = 1/24

(3x-4(12-x))/24 = 1/24

7x-48 = 1

7x = 49

X = 7

Therefore , it will take 7 hrs to fill the tank.