In an election, a candidate who gets 84 % of the votes is elected by a majority of 476 votes. What is the total number of votes polled ?

Options

A. 900
B. 810
C. 600
D. 700

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: We know that a candidate received 84% of the votes and won by a majority of 476 votes. The remaining candidate received the rest of the votes, which is 16%.

2. **Calculate the Vote Difference**: The difference in votes between the winning candidate and the losing candidate can be calculated as follows:
\[ \text{Difference in votes} = \text{Votes for winning candidate} - \text{Votes for losing candidate} \]
Since the winning candidate received 84% and the losing candidate received 16%, the difference is:
\[ 84\% - 16\% = 68\% \]

3. **Set Up the Equation**: We know that this difference (68% of the total votes) is equal to the majority by which the candidate won, which is 476 votes. Therefore, we can set up the equation:
\[ 68\% \text{ of Total Votes} = 476 \]

4. **Convert Percentage to Decimal**: To solve for the total number of votes, we convert 68% into decimal form:
\[ 68\% = \frac{68}{100} = 0.68 \]

5. **Solve for Total Votes**: Let \( V \) be the total number of votes. We can rewrite the equation as:
\[ 0.68V = 476 \]
To find \( V \), divide both sides by 0.68:
\[ V = \frac{476}{0.68} \]

6. **Calculate the Total Votes**: Now, perform the division:
\[ V = 700 \]

Thus, the total number of votes polled is **700**.