There were two candidates in an 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 $x$.
Votes not cast = $10\%$ of $x=0.1x$
Total votes cast = $90\%$ of $x=0.9x$
Invalid votes = $60$
Total valid votes = $0.9x-60$

Votes obtained by the winner = $47\%$ of total enrolled voters = $0.47x$
Votes obtained by the loser = $\text{Total valid votes}-\text{Winner’s votes}$

$$\text{Loser’s votes}=(0.9x-60)-0.47x=0.43x-60$$

The winner won by $308$ votes:

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

$$0.47x-(0.43x-60)=308$$

$$0.04x+60=308$$

$$0.04x=248$$

$$x=\frac{248}{0.04}=\frac{24800}{4}=6600$$

The number of enrolled voters is $6,600$.