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 the 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:

It will take 7 Hrs to fill the tank.

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 hours.

Therefore, each of the 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 hours for an empty tank to overflow.

∴ 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

∴It will take 7 Hrs to fill the tank.

Answer 2

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