Practice Questions
Concept Explanation
Election problems combine voter turnout (percentage of registered voters who voted) with vote share (percentage of valid votes a candidate received).
Turnout
Votes polled = (turnout%/100) × total registered voters.
Valid vs Invalid Votes
Valid votes = polled votes − invalid votes. A candidate's votes = vote share% of valid votes.
Winning Margin
Margin = winner's votes − runner-up's votes, often expressed as a percentage of valid votes.
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Q1 EasyOut of 8000 votes polled in an election, 5% were invalid. How many valid votes were there?ExplanationInvalid votes = 5% of 8000 = 400. Valid votes = 8000 − 400 = 7600.
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Q2 EasyIn an election with 10,000 registered voters, 70% of the voters cast their votes. How many votes were polled?ExplanationVotes polled = 70% of 10,000 = 7000.
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Q3 EasyTwo candidates receive 4500 and 3500 votes respectively out of 10,000 valid votes. What is the winner's vote share as a percentage of valid votes?ExplanationWinner's vote share = (4500/10,000) × 100 = 45%.
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Q4 EasyA candidate needs 50% of valid votes to win an election. If 12,000 valid votes are cast, what is the minimum number of votes required to win?ExplanationMinimum winning votes = 50% of 12,000 = 6000.
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Q5 MediumIn an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:ExplanationValid votes = 80% of 7500 = 6000. The other candidate got 45% of valid votes = 45% of 6000 = 2700.
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Q6 MediumIn an election between A and B, 25% of the votes are invalid. If A gets 60% of the valid votes, then B gets ____% of total votes polled.ExplanationValid votes = 75% of polled. B gets 40% of valid votes = 40% of 75% = 30% of total votes polled.
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Q7 MediumCandidate A received 55% of 7600 valid votes in an election. How many votes did candidate A receive?ExplanationVotes received by A = 55% of 7600 = 4180.
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Q8 MediumIn a constituency of 20,000 voters, 75% cast their votes and 4% of the polled votes were invalid. How many valid votes were there?ExplanationVotes polled = 15,000. Invalid votes = 600. Valid votes = 14,400.
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Q9 MediumThe winner secured 54% and the runner-up secured 42% of 10,000 valid votes. What was the winning margin in votes?ExplanationWinning margin = (54% − 42%) of 10,000 = 12% of 10,000 = 1200 votes.
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Q10 HardIn an election between two candidates, 15% of registered voters did not vote. 10% of the cast votes were declared invalid. The winner received 55% of the valid votes and won by 765 votes. How many total registered voters were there?ExplanationLet registered voters = V. Valid votes = 0.85V × 0.90 = 0.765V. Margin = (55% − 45%) of valid = 0.10 × 0.765V = 765 → V = 10,000.
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Q11 HardIn an election between two candidates, 15% of votes were invalid. The winner got 60% of the valid votes and won by 4800 votes. How many valid votes were polled?ExplanationWinner gets 60% and loser gets 40% of valid votes. Margin = 20% of valid votes = 4800 → valid votes = 24,000.
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Q12 HardIn an election, 10% of the voters in the voter list did not cast their vote, whereas 10% of the votes cast were found to be invalid. The winning candidate got 56% of the valid votes and won the election by a margin of 1458 votes. What is the total number of voters enrolled in the voter list?ExplanationLet enrolled voters = V. Valid votes = 0.90V × 0.90 = 0.81V. Margin = 12% of valid = 0.12 × 0.81V = 1458 → V = 15,000.
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Q13 HardIf 80% of 25,000 registered voters cast their votes and 5% of the polled votes are invalid, how many valid votes were cast?ExplanationVotes polled = 20,000. Invalid votes = 1000. Valid votes = 19,000.
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Q14 HardTurnout in an election is 72% and invalid votes are 2% of the polled votes. Valid votes as a percentage of registered voters is:ExplanationValid votes as a fraction of registered voters = 0.72 × 0.98 = 0.7056 = 70.56%.
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DS1 Easy
How many votes did candidate A receive in the election?
Statement ICandidate A received 55% of the valid votes cast.
Statement IIThere were 7600 valid votes in the election.
ExplanationA's votes = 55% of 7600 = 4180. Both the vote share and total valid votes are needed. -
DS2 Easy
What was the voter turnout in the election?
Statement IThe number of registered voters in the constituency was 10,000.
Statement IIThe number of votes polled in the election was 7000.
ExplanationTurnout = (7000/10,000) × 100 = 70%. Both registered voters and votes polled are needed.
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DS3 Easy
Did the candidate win a majority of the valid votes?
Statement IThe candidate received 6200 votes in the election.
Statement IIThe total number of valid votes cast was 10,000.
Explanation6200/10,000 = 62%, which is more than 50%. Both the candidate's votes and total valid votes are needed. -
DS4 Medium
How many valid votes were cast in the election?
Statement IA total of 8000 votes were polled in the election.
Statement II5% of the polled votes were declared invalid.
ExplanationValid votes = 8000 × 0.95 = 7600. Both the polled votes and invalid percentage are needed.