In an election between two candidates, 25% of the voters did not cast their votes. Of the votes cast, 10% were declared invalid. The winner got 55% of the valid votes and won by 2,700 votes. Find the total number of voters.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 40,000
With only two candidates, the loser gets 45% of the valid votes, so the margin is 10% of the valid votes. Work back from valid votes to all voters.
Valid votes \(=0.75\times0.9=0.675\) of the voters
Margin \(=10\%\) of valid votes \(=0.0675\) of the voters
Voters \(=2700\div0.0675=40000\)
There are 40,000 voters in all.
Why the other options are incorrect
Option (1) 4,000 — Incorrect. With 4,000 voters there are 2,700 valid votes, and the margin would be 270, not 2,700.
Option (2) 36,000 — Incorrect. With 36,000 voters there are 24,300 valid votes, and the margin would be 2,430, not 2,700.
Option (4) 30,000 — Incorrect. With 30,000 voters there are 20,250 valid votes, and the margin would be 2,025, not 2,700.