Question : In a two-candidate election, 10% of the voters did not cast their ballots. 10% of the votes cast were found invalid. The winning candidate received 54% of the valid votes and a 1620 vote majority. Find the number of people on the voter list who have registered to vote.
Option 1: 25000
Option 2: 26000
Option 3: 24500
Option 4: 25500
Correct Answer: 25000
Solution : Let $x$ be the total votes. Voters did not cast their ballots = 10% of $x$ Voters casted their votes = 90% of $x$ = $\frac{9x}{10}$ Invalid votes = 10% of $\frac{9x}{10}$ Valid votes = 90% of $\frac{9x}{10}$ = $\frac{81x}{100}$ Votes of winning candidate = 54% of $\frac{81x}{100}$ Votes of failed candidate = 46% of $\frac{81x}{100}$ Majority = 1620 Now, (54 – 46)% i.e., 8% of $\frac{81x}{100}$ = 1620 $\therefore x$ = $\frac{1620×100×100}{81×8}$ = 25000 Hence, the correct answer is 25000.
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Question : In an election between two candidates, 30% of the electorate did not cast their votes. 20% of the votes polled were found invalid. The winning candidate got 64% of the valid votes and won by a majority of 3136 votes. Find the number of voters enrolled in the voter list.
Option 1: 20000
Option 2: 25000
Option 3: 24000
Option 4: 30000
Question : In an election between two candidates, 85% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 6,936 votes which was 85% of the valid votes. Find the total number of voters enrolled in that election.
Option 1: 10,500
Option 2: 10,800
Option 3: 10,000
Option 4: 10,700
Question : In an election between two candidates, 80% of the voters cast their votes, out of which 5% votes were declared invalid. A candidate got 9500 votes which were 80% of the valid votes. Find the total number of voters enrolled in that election.
Option 1: 14780
Option 2: 15100
Option 3: 15625
Option 4: 16100
Question : In an election between two candidates, 65% of the voters cast their votes, out of which 3% of the votes were decided to be invalid. A candidate got 81,965 votes, which is 65% of the total valid votes. What is the total number of votes enrolled in that election?
Option 1: 2,00,000
Option 2: 1,90,000
Option 3: 2,15,000
Option 4: 1,85,000
Question : In an election, a candidate secures 42% of the votes polled but is defeated by his only opponent by a majority of 3080 votes, because of 1400 invalid votes. The percentage of invalid votes is _______.
Option 1: 5%
Option 2: 3%
Option 3: 4%
Option 4: 6%
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