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(A) Let the total number of voters enrolled be $x$.$10 \%$ of voters did not cast their vote,so votes polled $= 90 \%$ of $x = 0.9x$.$10 \%$ of the vo

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$25000$

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(A) Let the total number of voters enrolled be $x$.$10 \%$ of voters did not cast their vote,so votes polled $= 90 \%$ of $x = 0.9x$.$10 \%$ of the votes polled were invalid,so valid votes $= 90 \%$ of $0.9x = 0.81x$.The successful candidate received $54 \%$ of the valid votes,so the defeated candidate received $(100 - 54) \% = 46 \%$ of the valid votes.The difference in percentage of valid votes $= 54 \% - 46 \% = 8 \%$ of the valid votes.Given that the majority is $1620$ votes,we have: $8 \%$ of $0.81x = 1620$.$0.08 	imes 0.81x = 1620$.$0.0648x = 1620$.$x = \frac{1620}{0.0648} = 25000$.Thus,the total number of voters enrolled is $25000$.

In an election between two candidates,$10 \%$ of the voters did not cast their vote. $10 \%$ of the votes polled were found invalid. The successful candidate received $54 \%$ of the valid votes and won by a majority of $1620$ votes. The total number of voters enrolled on the voter's list was:

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