Let 150 workers complete work in $n$ days
$\therefore 150$ workers complete $\frac{1}{n}$ work in one day
1 worker complete $\frac{1}{150 n}$ work in one day
$\therefore 150$ workers complete $\frac{150}{150 n}$ work in one day
Since 4 workers are dropped on the second day.
On second day's work done by 146 worker
$=\frac{146}{150 n}$
On third day work done by 142 worker
$=\frac{142}{150 n}$
In this manner the work was finished in $n+8$ days.
$\therefore \frac{150}{150 n}+\frac{146}{150 n}+\frac{142}{150 n}+\ldots \ldots . \text { to }(n+8) \text { terms }=1$
or $\frac{1}{150 n}[150+146+142+\ldots \ldots$. to $(n+8)$ terms $]=1$
$\therefore 150+146+142+\ldots \ldots \ldots$ to $(n+8)$ term
$=150 n$
or $\frac{n+8}{2}[2 \times 150+(n+8-1)$ term $]=150 n$
$\Rightarrow \quad(\mathrm{n}+8)[300-4(\mathrm{n}+7)]=300 \mathrm{n}$
or $(n+8)(300-28-4 n)=300 n$
$\Rightarrow 2176+240 n-4 n^2=300 n$
or $4 n^2+60 n-2176=0$
$\Rightarrow \quad n^2+15 n-544=0$
or $\quad(n+32)(n-17)=0$
$\Rightarrow n=17$ and $n \neq-32$
$\therefore$ work was completed in $17+8=25$ days