Some workers could complete a work in $150$ days. However, due to the absence of $15$ workers it was completed in $165$ days. Then the initial number of workers was:

Let the initial number of workers be $x$.
The total work can be expressed in terms of man-days:

$$\text{Total Work}=\text{Number of workers}\times \text{Number of days}$$

$$\text{Total Work}=x\times 150=150x$$

According to the second condition, $15$ workers were absent, so the number of working people was $(x-15)$, and they completed the work in $165$ days:

$$\text{Total Work}=(x-15)\times 165$$

Since the total work remains constant, we equate the two expressions:

$$150x=165(x-15)$$

$$150x=165x-165\times 15$$

$$165\times 15=165x-150x$$

$$2475=15x$$

$$x=\frac{2475}{15}=165$$

Thus, the initial number of workers was $165$.