How to Solve Election and Votes Percentage Problems
Solve election vote-percentage aptitude problems: valid votes, candidate shares, and the winning-margin shortcut, with practice questions.
Expected Interview Answer
Election vote problems are solved by first isolating the valid votes (total votes minus invalid ones), then treating each candidate’s share as a straightforward percentage of that valid-vote total, and using the winning margin percentage to back out actual vote counts.
The first, most commonly skipped step is subtracting invalid or void votes from the total polled to get the valid vote base — percentages in these problems almost always apply to valid votes, not total votes cast. Once you have the valid-vote base V, a candidate winning p% of votes gets p%×V votes, and a margin of victory stated as m% of valid votes translates to m%×V actual votes separating the two candidates. For a two-candidate race, if the winner gets p% then the loser gets (100−p)%, so the margin percentage is (2p−100)%, letting you solve for p directly from a stated margin.
- Isolating valid votes first prevents the single most common setup error
- The margin-to-percentage shortcut (2p−100)% solves two-candidate races in one step
- The same percentage-of-a-subset method extends to elections with 3+ candidates
AI Mentor Explanation
A tournament’s total deliveries bowled include wides and no-balls that do not count as legal deliveries, just as an election’s total votes include invalid ballots that do not count toward any candidate — you must subtract those first to get the base for any percentage calculation. Once you have legal deliveries (valid votes), a bowler’s percentage of deliveries generating a wicket is computed against that legal-delivery base, exactly as an election candidate’s vote percentage is computed against valid votes only.
Worked example (invalid votes + margin)
Valid votes
- 100000×0.90 = 90,000
Winner (55%)
- 90000×0.55 = 49,500
Margin
- (55−45)% of 90000 = 9,000
Step-by-Step Explanation
Step 1
Find valid votes
Valid votes = Total votes polled − Invalid votes (often given as a percentage of total).
Step 2
Apply the candidate percentage
A candidate’s vote count = their % × valid votes, never total votes.
Step 3
Use the margin shortcut
In a two-candidate race, margin % = (2p − 100)% where p is the winner’s share.
Step 4
Solve for the requested unknown
Rearrange to find total votes, valid votes, or a candidate’s share as required.
What Interviewer Expects
- Correctly subtracting invalid votes before applying any percentage
- Understanding that vote percentages apply to valid votes, not total votes cast
- Using the margin-percentage shortcut for two-candidate races
- Extending the same method correctly to races with more than two candidates
Common Mistakes
- Applying a candidate’s percentage to total votes instead of valid votes
- Forgetting to subtract invalid votes at all
- Assuming the losing candidate’s percentage without checking for a third candidate
- Mixing up whether the given percentage is of the winner’s or loser’s votes
Best Answer (HR Friendly)
“The step people skip is subtracting invalid votes first — percentages in these problems apply to valid votes, not the raw total polled. Once I have that valid-vote base, a candidate’s share is just their percentage of it, and for a two-candidate race I use the shortcut that the margin percentage is twice the winner’s share minus 100, which lets me solve for the winner’s percentage directly from a stated margin.”
Follow-up Questions
- How would you extend this method to a three-candidate election?
- How do you find the total votes polled given only the winning margin count and percentage?
- What changes if invalid votes are given as a count rather than a percentage?
- How would you solve for the losing candidate’s vote count given the winner’s count and margin percentage?
MCQ Practice
1. In an election, 20% of 50,000 total votes were invalid. Candidate A got 60% of valid votes. How many votes did A get?
Valid votes = 50000×0.80 = 40,000. A got 40000×0.60 = 24,000.
2. Two candidates contest an election with no invalid votes. The winner gets 56% of the votes and wins by 4,800 votes. Total votes polled are?
Margin % = 56 − 44 = 12%. 12% of total = 4800 → total = 4800/0.12 = 40,000.
3. If invalid votes are 15% of total polled, what fraction of total polled do valid votes represent?
Valid votes = 100% − 15% = 85% of total polled.
Flash Cards
First step in any election-vote problem? — Subtract invalid votes from total polled to get valid votes.
What do candidate percentages apply to? — Valid votes, never the raw total votes polled.
Two-candidate margin shortcut? — Margin % = (2p − 100)%, where p is the winner’s valid-vote share.
How to find total polled from a margin count? — Total = margin count ÷ margin percentage (as a decimal).