In an election between two candidates, the one who gets 35% of the votes polled is defeated by 15000 votes. The number of votes polled by the winning candidate is?

Q) In an election between two candidates, the one who gets 35%
of the votes polled is defeated by 15000
votes. The number of votes polled by the winning candidate is?

Solving the Election Vote Problem: A Mathematical Approach

In any election, understanding the number of votes polled by each candidate can provide crucial insights into the dynamics of the race. In this scenario, we have a situation where a candidate who received 35% of the total votes was defeated by a margin of 15,000 votes. Our goal is to determine the number of votes polled by the winning candidate. Let’s dive into the solution step by step.

Problem Statement

In an election between two candidates:

• One candidate received 35% of the votes.
• This candidate was defeated by 15,000 votes.
• We need to find out the number of votes polled by the winning candidate.

Step-by-Step Solution

1. Understanding the Vote Distribution

Let’s assume the total number of votes polled is denoted by V.

• The votes polled by the defeated candidate, who received 35% of the total votes, is:

  $$\text{Votes polled by defeated candidate} = 0.35 \times V$$

• The remaining percentage of votes would have been polled by the winning candidate, which is:

  $$\text{Votes polled by winning candidate} = 0.65 \times V$$

2. Setting Up the Equation

According to the problem, the winning candidate won by a margin of 15,000 votes. This margin can be expressed as the difference between the votes polled by the winning candidate and the votes polled by the defeated candidate:

$$\text{Margin} = \text{Votes polled by winning candidate} - \text{Votes polled by defeated candidate}$$

Substituting the known values:

$$15000 = (0.65 \times V) - (0.35 \times V)$$

3. Simplifying the Equation

We can simplify the equation by combining like terms:

$$15000 = 0.65V - 0.35V$$ $$15000 = 0.30V$$

4. Solving for Total Votes (V)

To find the total number of votes polled (V), we divide both sides of the equation by 0.30:

$$V = \frac{15000}{0.30}$$ $$V = 50000$$

5. Determining the Votes Polled by the Winning Candidate

Now that we know the total number of votes polled is 50,000, we can easily determine the number of votes polled by the winning candidate:

$$\text{Votes polled by winning candidate} = 0.65 \times 50000$$ $$\text{Votes polled by winning candidate} = 32500$$

Conclusion

In this election, the winning candidate polled 32,500 votes. This mathematical approach not only helps in solving election-related problems but also serves as a fundamental technique in understanding percentages and vote distributions in various scenarios.

Understanding the distribution of votes and the margins in elections can provide valuable insights for candidates, campaigners, and voters alike. Whether you are analyzing past elections or planning for future ones, mastering these calculations is essential.