In an election between two candidates, 20% of the voters did not cast their votes. Of the votes cast, 12.5% were declared invalid. The winner got 60% of the valid votes and won by 5600 votes. Find the total number of voters.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40000
Each percentage is taken of the group left at the step before: votes cast from all voters, valid votes from the votes cast, and the winner’s share from the valid votes.
Let the number of voters \(=N\); votes cast \(=80\%\) of \(N=0.8N\)
Valid votes \(=87.5\%\) of \(0.8N=0.7N\)
Winner \(=60\%\), loser \(=40\%\) of the valid votes; margin \(=20\%\) of \(0.7N=0.14N\)
\(0.14N=5600\), so \(\displaystyle N=\frac{5600}{0.14}=40000\)
The total number of voters is 40000.