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 $24\text{hours}$, while each emptying pipe can empty the fully filled up tank in $18\text{hours}$. If the tank is full and all the pipes are opened simultaneously, the tank is emptied after $9\text{hours}$. The number of emptying pipes is:

Let the total number of emptying pipes be $x$.
Since there are $9$ pipes in total, the number of filling pipes will be $9-x$.

Given:

* Efficiency of one filling pipe = $+\frac{1}{24}$ per hour
* Efficiency of one emptying pipe = $-\frac{1}{18}$ per hour

When all pipes are opened together, a full tank is emptied in $9\text{hours}$, so the net work done per hour is $-\frac{1}{9}$.
Setting up the efficiency equation:

$$(9-x)\left(\frac{1}{24}\right)+x\left(-\frac{1}{18}\right)=-\frac{1}{9}$$

Multiply the entire equation by the LCM of $24,18$, and $9$, which is $72$:

$$72\times \frac{9-x}{24}-72\times \frac{x}{18}=72\times \left(-\frac{1}{9}\right)$$

$$3(9-x)-4x=-8$$

$$27-3x-4x=-8$$

$$27-7x=-8$$

$$27+8=7x$$

$$35=7x⟹x=5$$

Therefore, the number of emptying pipes is $5$.