In an election between two candidates, 75% of the voters cast their votes, out of which 2% votes were declared Invalid. Acandidate got 9261 votes which were 75% of the valid votes. The total number of voters enrolled in that election was

Options

A. 16000
B. 16400
C. 16800
D. 18000

Answer

To solve the problem step by step, we will follow the information given in the question and the video transcript.

### Step 1: Define the total number of voters
Let the total number of voters enrolled in the election be \( X \).

### Step 2: Calculate the number of voters who cast their votes
According to the question, 75% of the voters cast their votes. Therefore, the number of voters who cast their votes is:
\[ \text{Voters who cast votes} = 0.75X \]

### Step 3: Calculate the number of valid votes
Out of the votes cast, 2% were declared invalid. This means that 98% of the votes were valid. Therefore, the number of valid votes is:
\[ \text{Valid votes} = 0.98 \times (0.75X) = 0.735X \]

### Step 4: Relate the candidate's votes to valid votes
The candidate received 9261 votes, which is stated to be 75% of the valid votes. Therefore, we can set up the equation:
\[ 0.75 \times \text{Valid votes} = 9261 \]
Substituting the expression for valid votes:
\[ 0.75 \times (0.735X) = 9261 \]

### Step 5: Solve for \( X \)
Now, we simplify the equation:
\[ 0.75 \times 0.735X = 9261 \]
Calculating \( 0.75 \times 0.735 \):
\[ 0.55125X = 9261 \]
Now, divide both sides by 0.55125 to find \( X \):
\[ X = \frac{9261}{0.55125} \]
Calculating the right side:
\[ X \approx 16,800 \]

### Conclusion
The total number of voters enrolled in that election was \( 16,800 \).

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