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.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 6860.
Let the total number of voters be N
12% of the voters did not cast their votes, so 88% of the voters cast their votes.
Number of voters who cast their votes = 0.88 × N
Out of the voters who cast their votes, 84 voters cast blank ballots.
Therefore, the number of valid votes is 0.88N - 84
Ramagya won with 54% of all the voters supporting him
Votes for Ramagya = 0.54N
Since the remaining valid votes went to Shravan, votes for Shravan = 0.88N − 84 − 0.54N
⇒ 0.34N - 84
According to the question, Ramagya received 1456 more votes than Shravan
⇒ 0.54N - (0.34N - 84) = 1456
⇒ 0.54N - 0.34N + 84 = 1456
⇒ 0.20N = 1456 - 84
⇒ 0.20N = 1372
⇒ N = 1372/0.20
⇒ N = 6860
So, the total number of voters in the list is 6860.