A single person takes $6\text{ minutes}$ to fill a bottle. If from $11\text{ am}$ to $12.30\text{ pm}$ $1845$ bottles are to be filled, how many persons should be employed on this job?

The total timeframe from $11:00\text{ AM}$ to $12:30\text{ PM}$ is $1\text{ hour and }30\text{ minutes}=90\text{ minutes}$.
Since 1 person fills 1 bottle in $6\text{ minutes}$, the rate of work of 1 person is $\frac{1}{6}$ bottles per minute.

Let $N$ be the number of people required to fill $1845$ bottles in $90\text{ minutes}$:

$$\text{Total Work}=\text{Number of people}\times \text{Rate of one person}\times \text{Total time}$$

$$1845=N\times \left(\frac{1}{6}\right)\times 90$$

$$1845=N\times 15$$

$$N=\frac{1845}{15}=123$$

Thus, $123$ persons should be employed.