There were two candidates in the election. $10\%$ of voters did not cast their votes. $60$ votes were found invalid. The winning candidate got $47\%$ of the total votes and won by $308$ votes. Find the number of voters enrolled.

Let the total number of enrolled voters be $100x$.
* Voters who cast their votes $=90\%$ of $100x=90x$
* Number of valid votes cast $=90x-60$
* Votes obtained by the winning candidate $=47\%$ of total votes $=47x$

Therefore, the votes obtained by the losing candidate will be:

$$\text{Loser’s Votes}=\text{Valid Votes}-\text{Winner’s Votes}$$

$$\text{Loser’s Votes}=(90x-60)-47x=43x-60$$

The winner won by a margin of $308$ votes:

$$\text{Winner’s Votes}-\text{Loser’s Votes}=308$$

$$47x-(43x-60)=308$$

$$4x+60=308$$

$$4x=248⟹x=62$$

The total number of enrolled voters is:

$$\text{Total Enrolled Voters}=100x=100\times 62=6,200$$