This question involves calculating the number of votes for the winning candidate in an election based on the percentage of votes received by the losing candidate and the margin of defeat.

Understanding the Election Scenario

We are given information about an election between two candidates:

• One candidate received 30% of the total votes.
• This candidate lost the election by a margin of 15,000 votes.

We need to find the number of votes obtained by the winning candidate.

Election Vote Calculation Steps

Let's break down the calculation step-by-step:

1. Determine the Percentage Share of Both Candidates

If one candidate received 30% of the total votes, and there are only two candidates, the winning candidate must have received the remaining percentage of votes.

• Losing Candidate's Share = 30%
• Winning Candidate's Share = 100% - Losing Candidate's Share
• Winning Candidate's Share = 100% - 30% = 70%

2. Calculate the Difference in Percentage

The difference in the percentage of votes between the winning and losing candidates is:

• Percentage Difference = Winning Candidate's Share - Losing Candidate's Share
• Percentage Difference = 70% - 30% = 40%

3. Relate Percentage Difference to Vote Difference

We are told that the losing candidate was defeated by 15,000 votes. This difference in votes corresponds to the percentage difference calculated above.

• So, 40% of the total votes is equal to 15,000 votes.

4. Calculate the Total Number of Votes

Let $T$ represent the total number of votes cast in the election. We can set up the following equation:

$40\% \times T = 15,000$

To express this mathematically:

$\frac{40}{100} \times T = 15,000$

Now, we solve for $T$:

$T = \frac{15,000 \times 100}{40}$

$T = \frac{1,500,000}{40}$

$T = 37,500$

Therefore, the total number of votes cast in the election was 37,500.

5. Calculate the Votes for the Winning Candidate

The winning candidate secured 70% of the total votes ($T$).

Number of votes for the winning candidate = 70% of $T$

$ \text{Winning Votes} = \frac{70}{100} \times 37,500 $

$ \text{Winning Votes} = 0.70 \times 37,500 $

$ \text{Winning Votes} = 26,250 $

Conclusion

The winning candidate obtained 26,250 votes.