In an election between two candidates, 10% of the voters did not cast their vote and 5% of the votes polled were found invalid. The successful candidate got 55% of the valid votes and won by a majority of 1,710 votes. The number of voters enrolled on the voters list was:

Let the total number of voters enrolled on the voters list be x.
Number of voters who cast their votes (90% of total):

Polled Votes=0.90x
Out of the polled votes, 5% were invalid, so 95% were valid:

Valid Votes=0.95×0.90x=0.855x
The successful candidate got 55% of the valid votes. Therefore, the losing candidate got (100%−55%)=45% of the valid votes.
The majority by which the winner won is the difference in their vote percentages:

Majority=55%−45%=10% of valid votes
Given that the majority is 1,710 votes:

10% of 0.855x=1710
0.10×0.855x=1710
0.0855x=1710
x=
0.0855
1710
​
=
855
1710×10000
​

Since 1710=855×2:

x=2×10000=20,000
The total number of voters enrolled was 20,000.