In an election, 12% of the voters in the voter list did not cast their votes, whereas 84 voters cast their ballot papers blank. There were only two candidates: Ramagya and Shravan. The winner, Ramagya, was supported by 54% of all the voters in the list. He got 1456 more votes than his rival, Shravan. Find the total number of voters in the list.

The correct answer is 6860.

Step 1: Define the variable.

Let $N$ be the total number of voters in the voter list.

Step 2: Calculate the total number of votes cast.

Given that 12% of the voters in the list did not cast their votes, the percentage of voters who cast their votes is:

$100\%-12\%=88\%$

Total number of votes cast = $0.88N$

Step 3: Calculate the number of valid votes for candidates.

Out of the total votes cast, 84 voters cast blank ballot papers. Therefore, the total valid votes cast for the two candidates are:

$0.88N-84$

Step 4: Express the votes received by Ramagya and Shravan.

Ramagya was supported by 54% of all the voters in the list:

$\text{Votes for Ramagya}=0.54N$

Shravan received the remaining valid votes:

$\text{Votes for Shravan}=(0.88N-84)-0.54N$

$\text{Votes for Shravan}=0.34N-84$

Step 5: Set up and solve the equation using the vote difference.

Ramagya received 1456 more votes than Shravan:

$\text{Votes for Ramagya}-\text{Votes for Shravan}=1456$

$0.54N-(0.34N-84)=1456$

$0.54N-0.34N+84=1456$

$0.20N+84=1456$

$0.20N=1456-84$

$0.20N=1372$

$N=\frac{1372}{0.20}$

$N=6860$

Therefore, the total number of voters in the list is 6860.