In an election, the votes cast for two candidates were in the ratio 4: 9. If the successful candidate received 984321 votes, then the total votes polled were:

Options

A. 1712597
B. 1421797
C. 1912577
D. 1571279

Answer

To solve the problem, we need to find the total votes polled in an election where the votes for two candidates are in the ratio of 4:9, and the successful candidate received 984321 votes.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The votes for the two candidates are in the ratio of 4:9. This means that if the first candidate received 4 parts of the votes, the second candidate received 9 parts.

2. **Identify the Successful Candidate**:
The successful candidate received 984321 votes. According to the ratio, the successful candidate corresponds to the larger part of the ratio, which is 9.

3. **Set Up the Equation**:
Let the total number of votes be represented as \( x \). According to the ratio:
- Votes for the first candidate = \( \frac{4}{13}x \) (since 4 + 9 = 13 parts)
- Votes for the second candidate = \( \frac{9}{13}x \)

Since the successful candidate received 984321 votes, we can set up the equation:
\[ \frac{9}{13}x = 984321 \]

4. **Solve for Total Votes \( x \)**:
To find \( x \), we can rearrange the equation:
\[ x = 984321 \times \frac{13}{9} \]

5. **Calculate \( x \)**:
First, calculate \( \frac{13}{9} \):
\[ \frac{13}{9} \approx 1.4444 \]
Now multiply:
\[ x = 984321 \times 1.4444 \approx 1420000 \]

6. **Final Answer**:
The total votes polled were approximately 1420000.