In an election between two candidates, the candidate who gets 35% of the votes polled is defeated by 15,900 votes. What is the total number of votes polled?

The correct answer is 53,000.

Step-by-step Explanation:

Let the total number of votes polled in the election be 100%.

Step 1: Find the percentage of votes obtained by the winning candidate.
The defeated candidate received 35% of the total votes polled.
Therefore, the winning candidate received the remaining percentage of votes:

$\text{Winning Candidate's Votes}=100\%-35\%=65\%$

Step 2: Determine the margin of defeat in percentage.
The difference in vote percentage between the winner and the loser is:

$\text{Margin of Defeat}=65\%-35\%=30\%$

Step 3: Calculate the total number of votes polled.
We are given that the candidate was defeated by 15,900 votes, which means 30% of the total votes equals 15,900.

$30\%\text{of Total Votes}=\mathrm{15,900}$

$\frac{30}{100}\times \text{Total Votes}=\mathrm{15,900}$

$\text{Total Votes}=\frac{\mathrm{15,900}\times 100}{30}$

$\text{Total Votes}=530\times 100=\mathrm{53,000}$

Therefore, the total number of votes polled in the election is 53,000.