Question

Q53 Nine pipes are attached to a tank, of which
some are emptying pipes and some are
filling pipes. Each filling pipe can fill the
empty tank in 24 hours, while each
emptying pipe can empty the fully filled
up tank in 18 hours. If the tank is full and
all the pipes are opened simultaneously,
the tank is emptied after 9 hours. The
number of emptying pipes is:

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Answer 1

Step-by-step explanation:

Let the number of fill pipes be 'n'. Therefore, there will be (8 - n) waste pipes.

Each fill pipe fills 1818th of the tank in an hour. So, "n" fill pipes will fill n8n8th of the tank in an hour.

Each waste pipe drains 1616th of the tank in a hour.

So, \"8 - n\" waste pipes will drain 8−n68−n6th of the tank in an hour.

Keeping these 8 pipes open results in 1616th of the tank being drained every hour.

Hence, n8−8−n6=−16n8−8−n6=−16

Solving for n, we get n = 4.

Therefore, there are 4 fill pipes and 4 waste pipes