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

The time available from 11 am to 12.30 pm is $1\text{hour and }30\text{minutes}=90\text{minutes}$.
A single person takes $6\text{minutes}$ to fill $1\text{bottle}$.
Therefore, in $90\text{minutes}$, one person can fill:

$$\text{Bottles filled by 1 person}=\frac{90}{6}=15\text{bottles}$$

We need to fill a total of $1845$ bottles in that time period. Let the number of persons required be $N$:

$$N=\frac{\text{Total Bottles}}{\text{Bottles filled by 1 person}}=\frac{1845}{15}=123\text{persons}$$