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.
Answer & explanation
Correct answer: option 1
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