Two candidates contested an election. 20% of the votes were declared invalid. The winner got 70% of the valid votes and won by 9,600 votes. Find the total number of votes.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30000
With only two candidates, the loser gets the other 30% of the valid votes, so the winning margin is \(70\%-30\%=40\%\) of the valid votes.
Let the total votes be \(V\); valid votes \(=80\%\) of \(V=0.8V\)
Margin \(=40\%\) of \(0.8V=0.32V\)
\(0.32V=9600\), so \(\displaystyle V=\frac{9600}{0.32}=30000\)
The total number of votes is 30,000.