Question : In an election between two candidates, the difference between the candidates who won and lost was 2,500 votes. The candidate who won got 75% of the votes, and there were no invalid votes. The total number of votes polled by the losing candidate was:
Option 1: 1875
Option 2: 5000
Option 3: 1250
Option 4: 3750
Correct Answer: 1250
Solution : Let V be the total number of votes polled. The winning candidate received 75% of the votes, which is 0.75V. ⇒ The losing candidate received the remaining 25% of the votes, which is 0.25V. The difference between the votes of the winning and losing candidates is 2,500. ⇒ 0.75V - 0.25V = 2,500 ⇒ 0.5V = 2,500 ⇒ V = $\frac{2,500}{0.5}$ ⇒ V = 5,000 ⇒ The losing candidate received 0.25 × 5,000 = 1,250 votes Hence, the correct answer is 1250.
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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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