In a two-candidate election, 10% of the voters did not cast their ballots. 10% of the votes cast were found invalid. The winning candidate received 54% of the valid votes and a 1620-vote majority. Find the number of people on the voter list who have registered to vote.

25000

Let, total enrolled voter be x

10% did not cast vote means casted or polled vote = \(\frac{9x}{10}\)

10% vote is invalid , valid vote = \(\frac{9x}{10}\) × \(\frac{90}{100}\)

⇒ \(\frac{81x}{100}\)

The winner candidate got 54% of the polled vote means loosed got (100 – 54) = 46% vote

Winer candidate got total {\(\frac{54}{100}\) × \(\frac{81x}{100}\)} vote

And the looser candidate got {\(\frac{46}{100}\) × \(\frac{81x}{100}\)} vote

Accordingly,

 {\(\frac{54}{100}\) × \(\frac{81x}{100}\)} -  {\(\frac{46}{100}\) × \(\frac{81x}{100}\)} = 1620

⇒  \(\frac{81x}{100}\)  ×  \(\frac{54-46}{100}\) = 1620

⇒ x  = \(\frac{1620 × 10000}{81 × 8}\) = 25000