There were two candidates in an election. `75%` of voters cast their votes, out of which `2%` of the votes were found invalid. A candidate got 9261 votes which were `75%` of total valid votes. Find the total number of voters enrolled.

Answer

To solve the problem step by step, we will follow the logical flow of the information provided in the question.

### Step 1: Define the total number of voters enrolled
Let the total number of voters enrolled 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 invalid votes
Out of the votes cast, \( 2\% \) were found to be invalid. Thus, the number of invalid votes can be calculated as:
\[ \text{Invalid votes} = 0.02 \times (0.75x) = 0.015x \]

### Step 4: Calculate the number of valid votes
The total number of valid votes is the total votes cast minus the invalid votes:
\[ \text{Valid votes} = \text{Votes cast} - \text{Invalid votes} = 0.75x - 0.015x = 0.735x \]

### Step 5: Relate the candidate's votes to valid votes
We know that one candidate received \( 9261 \) votes, which is \( 75\% \) of the total valid votes. Therefore, we can set up the equation:
\[ 9261 = 0.75 \times (0.735x) \]

### Step 6: Solve for \( x \)
Now, we can solve the equation for \( x \):
\[ 9261 = 0.75 \times 0.735x \]
\[ 9261 = 0.55125x \]
\[ x = \frac{9261}{0.55125} \]
Calculating this gives:
\[ x \approx 16800 \]

### Conclusion
Thus, the total number of voters enrolled is \( 16800 \).

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