Calculating Vote Percentage Difference
The problem requires finding the difference in vote percentages between the winning candidate and the runner-up in an election.
Step 1: Calculate Total Votes
First, sum the votes received by all four candidates to find the total number of valid votes polled.
Total Votes = 4500 + 1260 + 240 + 2000 = 8000
Step 2: Identify Winning and Runner-up Candidates
Identify the candidate with the highest votes (winner) and the candidate with the second-highest votes (runner-up).
- Winning Candidate Votes: 4500
- Runner-up Candidate Votes: 2000
Step 3: Calculate the Difference in Votes
Find the difference between the votes received by the winner and the runner-up.
Difference in Votes = 4500 - 2000 = 2500
Step 4: Calculate Percentage Difference
Calculate the percentage difference relative to the total votes polled.
Percentage Difference = (Difference in Votes / Total Votes) \(\times\) 100
Percentage Difference = (\( \frac{2500}{8000} \)) \(\times\) 100
Percentage Difference = (\( \frac{25}{80} \)) \(\times\) 100
Percentage Difference = (\( \frac{5}{16} \)) \(\times\) 100
Percentage Difference = \( \frac{500}{16} \) %
Percentage Difference = \( 31.25 \) %
Conclusion
The difference between the vote percentages of the winning candidate and the runner-up candidate is 31.25%.
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