There are two candidates in an election `10%` of the voters did not cast their votes and 60 voters cast their voted to NOTA. The winners was suported by `47%` of the all votes in the list and he got `308` votes more than his rival. Find total votes ?

Options

A. `6800`
B. `6200`
C. `6600`
D. `6400`

Answer

To solve the problem step by step, let's denote the total number of voters as \( T \).

### Step 1: Calculate the total number of voters who cast their votes
Given that \( 10\% \) of the voters did not cast their votes, this means \( 90\% \) of the voters did vote. Therefore, the number of voters who cast their votes is:
\[ \text{Voters who voted} = 0.9T \]

### Step 2: Account for NOTA votes
We know that \( 60 \) voters cast their votes for NOTA (None of the Above). Therefore, the number of valid votes (votes for the candidates) is:
\[ \text{Valid votes} = 0.9T - 60 \]

### Step 3: Determine the votes for the winner
The winner received \( 47\% \) of all the votes in the list. Thus, the number of votes the winner received is:
\[ \text{Votes for winner} = 0.47T \]

### Step 4: Determine the votes for the rival
Since there are two candidates, the votes for the rival can be calculated as:
\[ \text{Votes for rival} = \text{Valid votes} - \text{Votes for winner} = (0.9T - 60) - 0.47T \]
This simplifies to:
\[ \text{Votes for rival} = 0.9T - 60 - 0.47T = 0.43T - 60 \]

### Step 5: Set up the equation based on the difference in votes
According to the problem, the winner received \( 308 \) votes more than the rival. Therefore, we can set up the equation:
\[ 0.47T = (0.43T - 60) + 308 \]

### Step 6: Simplify the equation
Now, we simplify the equation:
\[ 0.47T = 0.43T - 60 + 308 \]
\[ 0.47T = 0.43T + 248 \]
Subtract \( 0.43T \) from both sides:
\[ 0.04T = 248 \]

### Step 7: Solve for \( T \)
Now, divide both sides by \( 0.04 \):
\[ T = \frac{248}{0.04} = 6200 \]

### Conclusion
The total number of voters is \( \boxed{6200} \).

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