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 Easy
In an election with 10,000 registered voters, 70% voted. How many votes were polled?
Explanation70% of 10,000 = 7,000. -
Q2 Medium
Out of 8,000 votes polled, 5% were invalid. How many valid votes were there?
ExplanationInvalid = 400. Valid = 8,000 − 400 = 7,600. -
Q3 Medium
Candidate A got 55% of 7,600 valid votes. How many votes did A receive?
Explanation55% of 7,600 = 4,180. -
Q4 Medium
In a constituency of 20,000 voters, 75% cast votes and 4% were invalid. Valid votes are:
ExplanationPolled = 15,000. Invalid = 600. Valid = 14,400. -
Q5 Easy
Candidate P wins 60% and candidate Q gets 35% of valid votes. What percent of valid votes are unaccounted for by P and Q?
ExplanationRemaining = 100% − 95% = 5%. -
Q6 Easy
A candidate needs 50% of valid votes to win. If 12,000 valid votes are cast, minimum winning votes are:
Explanation50% of 12,000 = 6,000. -
Q7 Easy
In an election, 65% of 50,000 voters voted. Votes polled were:
Explanation65% of 50,000 = 32,500.
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Q8 Medium
Winner got 54% and loser got 42% of 10,000 valid votes. The winning margin is:
ExplanationMargin = (54% − 42%) of 10,000 = 12% of 10,000 = 1,200. -
Q9 Hard
If 80% of 25,000 registered voters cast votes and 5% of polled votes are invalid, valid votes are:
ExplanationPolled = 20,000. Invalid = 1,000. Valid = 19,000. -
Q10 Easy
Two candidates receive 4,500 and 3,500 of 10,000 valid votes. The winner's vote share is:
ExplanationWinner share = (4,500/10,000) × 100 = 45%. -
Q11 Hard
In a poll, 60% of 15,000 voters voted. If candidate X got 40% of valid votes and 3% were invalid, X's votes are approximately:
ExplanationPolled = 9,000. Valid = 9,000 × 0.97 = 8,730. X = 40% of 8,730 = 3,492 ≈ 3,480 (closest option). -
Q12 Hard
Turnout is 72% and invalid votes are 2% of polled votes. Valid votes as a percent of registered voters is:
ExplanationValid fraction = 0.72 × 0.98 = 0.7056 → 70.56%. -
Q13 Hard
A candidate secures 46% of valid votes and loses by 800 votes. Total valid votes are:
ExplanationWinner gets 54%, loser 46%. Gap = 8% of total = 800 → total valid votes = 10,000. -
Q14 Medium
In an election, 90% of 10,000 voters are registered valid voters and 80% of them vote. Votes polled are:
ExplanationRegistered valid = 9,000. Polled = 80% of 9,000 = 7,200.
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DS1 Easy
How many votes did candidate A receive?
Statement IA got 55% of valid votes.
Statement IIThere were 7,600 valid votes.
ExplanationA's votes = 55% of 7,600 = 4,180. Both needed. -
DS2 Medium
How many valid votes were cast?
Statement I8,000 votes were polled.
Statement II5% of polled votes were invalid.
ExplanationValid = 8,000 × 0.95 = 7,600.
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DS3 Easy
What is the turnout?
Statement IRegistered voters = 10,000.
Statement IIVotes polled = 7,000.
ExplanationTurnout = (7,000/10,000) × 100 = 70%. Both needed. -
DS4 Easy
Did the candidate win a majority of valid votes?
Statement IThe candidate received 6,200 votes.
Statement IITotal valid votes were 10,000.
Explanation6200/10000 = 62% > 50%. Both needed to confirm majority.