In an election between two candidates, a candidate who gets 64% of the votes polled is elected by a majority of 252 votes. What is the total number of votes polled?
900
Understanding the Election Vote Problem
This question asks us to find the total number of votes polled in an election given the percentage of votes for the winning candidate and the majority by which they won. We have two candidates contesting the election.
Calculating Votes for Each Candidate
Let's assume the total number of votes polled is $V$.
- The winning candidate received 64% of the votes polled.
- Votes for the winning candidate $= 64\% \text{ of } V = \frac{64}{100} V = 0.64V$.
- Since there are only two candidates, the other candidate (the loser) received the remaining percentage of votes.
- Percentage of votes for the losing candidate $= 100\% - 64\% = 36\%$.
- Votes for the losing candidate $= 36\% \text{ of } V = \frac{36}{100} V = 0.36V$.
Determining the Majority Votes
The majority is the difference between the votes received by the winning candidate and the votes received by the losing candidate. We are given that the majority is 252 votes.
Majority votes = Votes for winning candidate - Votes for losing candidate
So, we can set up the equation:
\( 0.64V - 0.36V = 252 \)
Solving for the Total Votes Polled
Now, we solve the equation for \(V\), the total number of votes polled.
Combine the terms with \(V\):
\( (0.64 - 0.36)V = 252 \)
\( 0.28V = 252 \)
To find \(V\), divide both sides by 0.28:
\( V = \frac{252}{0.28} \)
To simplify the division, we can multiply the numerator and denominator by 100 to remove the decimal:
\( V = \frac{252 \times 100}{0.28 \times 100} \)
\( V = \frac{25200}{28} \)
Now, perform the division:
\( 25200 \div 28 = 900 \)
So, \( V = 900 \).
The total number of votes polled is 900.
Verification
Let's check our answer:
- Total votes polled = 900
- Votes for the winner = 64% of 900 = \( 0.64 \times 900 = 576 \)
- Votes for the loser = 36% of 900 = \( 0.36 \times 900 = 324 \)
- Majority = Votes for winner - Votes for loser = \( 576 - 324 = 252 \)
The calculated majority (252) matches the given majority in the question, confirming our answer is correct.
Therefore, the total number of votes polled is 900.
Revision Table: Key Election Terms
| Term | Explanation |
|---|---|
| Total Votes Polled | The total count of valid votes cast in an election. |
| Majority | The number of votes by which the winning candidate exceeds the votes of the nearest rival. |
| Percentage of Votes | A candidate's votes expressed as a proportion of the total votes polled, multiplied by 100. |
Additional Information on Election Calculations
Understanding election results often involves dealing with percentages and majorities. Here are a few related concepts:
- Invalid Votes: Sometimes, a percentage of votes polled might be declared invalid. These are typically excluded from the calculation of votes for candidates. In this problem, we assumed all polled votes were valid and distributed between the two candidates.
- Electorate vs. Polled Votes: The total number of eligible voters (electorate) is often different from the total votes polled, as not everyone eligible may vote. This problem specifically deals with "votes polled".
- Winning Margin: Similar to majority, it's the difference in votes.
- Proportional Representation: An electoral system where parties gain seats in proportion to the number of votes cast for them. This differs from the simple majority system implied here.
Calculations like these help in understanding election outcomes and voter behaviour based on percentages and absolute vote counts.
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