In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes?

Options

A. 16800
B. 15800
C. 16700
D. 15700

Answer

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

### Step 1: Define the total number of votes
Let the total number of votes be \( T \).

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

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

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

### Step 5: Solve for \( T \)
Now we can solve for \( T \):
\[ 9261 = 0.75 \times 0.735T \]
\[ 9261 = 0.55125T \]
To find \( T \), divide both sides by 0.55125:
\[ T = \frac{9261}{0.55125} \approx 16800 \]

### Conclusion
Thus, the total number of votes is:
\[ \boxed{16800} \]