In an election, $12\%$ of the voters on the voters' list did not cast their votes, while $84$ voters cast blank ballots. There were only two candidates, Ramagya and Shravan. The winner, Ramagya, received the support of $54\%$ of all the voters on the list. He received $1456$ votes more than his rival, Shravan. Find the total number of voters on the list.

Let the total number of voters on the list be $100x$.
1. Voters who did not cast their vote $=12\%$ of $100x=12x$.
2. Total votes cast $=100x-12x=88x$.
3. Since $84$ ballots were blank, the total valid votes distributed between the two candidates:

$$\text{Total valid votes}=88x-84$$

4. Votes received by the winner (Ramagya) $=54\%$ of total voters $=54x$.
5. Votes received by the loser (Shravan):

$$\text{Shravan’s votes}=\text{Total valid votes}-\text{Ramagya’s votes}$$

$$\text{Shravan’s votes}=(88x-84)-54x=34x-84$$

6. The difference between their votes is given as $1456$:

$$\text{Ramagya’s votes}-\text{Shravan’s votes}=1456$$

$$54x-(34x-84)=1456$$

$$20x+84=1456$$

$$20x=1456-84$$

$$20x=1372$$

$$x=\frac{1372}{20}=68.6$$

7. Total number of voters on the list:

$$\text{Total voters}=100x=100\times 68.6=6860$$