Election Based Percentage: Vote Calculation Questions

Election Based Percentage questions use percentages to calculate total votes, votes received by candidates, winning margins, turnout and invalid votes. The main method is to express each candidate’s votes as a percentage of valid votes and then apply the given difference or total. These questions may involve two candidates, multiple candidates, polling percentages or rejected votes.

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What Is Election Based Percentage?

Election Based Percentage refers to vote-based problems in which candidate votes, winning margins, turnout or rejected votes are represented as percentages. The percentage base may be total votes polled, valid votes or the total electorate, so the base must be identified before calculation.

If a candidate receives p% of a total of V votes, the candidate’s votes are (p/100) × V. For two candidates, the difference in their vote percentages multiplied by the valid votes gives the winning margin. For example, if two candidates receive 54% and 46% of 20,000 valid votes, the margin is 8% × 20,000 = 1,600 votes.

Election Based Percentage Formula & Tricks

Important Formulas

Candidate votes
Candidate votes = (Candidate percentage/100) × Total votes

Use the total represented by the percentage as the base. It may be valid votes, votes polled or total electorate.

Winning margin
Margin = [(Winner percentage − Loser percentage)/100] × Total valid votes

For two candidates, subtract the loser’s percentage from the winner’s percentage and apply the difference to valid votes.

Total votes from margin
Total valid votes = Margin × 100/(Winner percentage − Loser percentage)

This formula applies when the percentage difference and the numerical winning margin are known.

Votes polled from turnout
Votes polled = (Turnout percentage/100) × Total electorate

Turnout percentage is calculated on the total number of registered voters or electors.

Valid votes after rejected votes
Valid votes = Votes polled × (100 − Rejected vote percentage)/100

First calculate votes polled from turnout, then remove the rejected or invalid votes.

Quick Tricks

Use the percentage difference for a two-candidate margin

Do not calculate both vote totals when only the margin is required. Subtract the two vote percentages and multiply the difference by total valid votes.

Example: If the candidates receive 58% and 42% of 25,000 valid votes, margin = 16% of 25,000 = 4,000 votes.
Assume 100 votes for percentage comparison

When only percentages are given, take the total as 100. This makes the ratio of votes clear before converting it to the actual total.

Example: Percentages 52%, 28% and 20% represent 52, 28 and 20 votes out of every 100 valid votes. Their ratio is 13:7:5.
Separate turnout from candidate share

Turnout is based on the total electorate, while a candidate’s percentage is usually based on valid votes. Calculate these stages separately.

Example: For 50,000 electors with 80% turnout and 5% invalid votes, valid votes = 50,000 × 0.80 × 0.95 = 38,000.

Election Based Percentage Concepts

Candidate Votes from Total Valid Votes

A candidate’s votes equal the stated percentage of the total valid votes when the question defines the candidate percentage on valid votes.

Use Candidate votes = (percentage/100) × total valid votes. If the result is a fraction, check whether the given data can represent whole votes; exact election data normally produces an integer vote count.

Example: In an election with 36,000 valid votes, a candidate receiving 47% gets (47/100) × 36,000 = 16,920 votes.

Winning Margin Between Two Candidates

For two candidates, the winning margin is the percentage-point difference between their shares multiplied by the total valid votes.

If the winner receives w% and the loser receives l%, then margin = (w − l)% of valid votes. The percentage difference is measured in percentage points; it is not a percentage increase from the loser’s votes.

Example: If A receives 55% and B receives 45% of 18,000 valid votes, A wins by 10% of 18,000 = 1,800 votes.

Finding Total Votes from the Winning Margin

When the numerical margin and the candidates’ percentage difference are known, total valid votes equal the margin divided by the percentage difference expressed as a decimal.

Use Total valid votes = Margin × 100/(winner percentage − loser percentage). If the winner leads by 2,400 votes with a 12-percentage-point lead, total valid votes = 2,400 × 100/12 = 20,000.

Example: A candidate wins by 3,500 votes after obtaining 57.5% against 42.5%. The difference is 15 percentage points, so valid votes = 3,500 × 100/15 = 23,333⅓. Since votes must be whole numbers, such data would be inconsistent for an exact election.

Turnout, Invalid Votes and Valid Votes

Turnout calculates votes polled from the total electorate, while invalid-vote percentage converts votes polled into valid votes.

Apply the operations in order: Votes polled = electorate × turnout percentage, followed by Valid votes = votes polled × (100 − invalid percentage)/100. Candidate percentages should then be applied to valid votes if the question states that they are based on valid votes.

Example: Among 40,000 electors, turnout is 75% and 4% of polled votes are invalid. Votes polled = 30,000; valid votes = 30,000 × 96/100 = 28,800.

Percentage Shares in a Multi-Candidate Election

In a multi-candidate election, each candidate’s votes are calculated from the same stated base, usually total valid votes, and all candidate percentages must add to 100% if no other category exists.

For candidates receiving p%, q% and r%, their vote ratio is p:q:r. If the percentages sum to less than 100%, the remaining percentage belongs to other candidates or an unspecified category.

Example: If three candidates receive 45%, 35% and 20% of 24,000 valid votes, their votes are 10,800, 8,400 and 4,800 respectively.

Election Based Percentage Video Lessons

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Election-Based Percentage Problems

Learn to solve percentage problems based on election results, including vote shares, valid votes, winning margins and changes in candidate support.

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Practice Election Based Percentage Questions

Practise published questions related to this topic.

1DMART is offering Buy 2, get 29 free on grocery items. What is the net percentage discount being offered by DMART? (Correct up to two decimal places)→ 2Find the single discount equivalent to two successive discounts of 29% and 28%.→ 350 percent of selling price of an article is equal to the 4/5 of the cost price of the article. What is the profit percentage?→ 4An item is sold for ₹7,200 after two successive discounts of 36% and 10%. What is the marked price (in ₹) of the item?→ 5Which of the following number is NOT divisible by 11 ?→ 6A person sells an article at the profit of 10 percent. Cost price and selling price both are increased by 20 percent. What will be the new profit percentage?→ 7If a four-digit number 34X1 is divisible by 7, then X2 is:→ 8There are 156 boy students and 143 girl students in a school. The principal wants to divide them in sections, such that a section can have only boys or only girls. If all sections should have the same number of students, and the principal wants to have as fewer sections as possible, how many sections would be there in the school?→ 9Simplify: √(2061 - √(1268 + √(850 - 66)))→ 10What is the Highest Common Factor of 15, 25 and 35?→

Election Based Percentage Quick Quiz

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Quick Revision Notes

Election Based Percentage Revision Points

Use these rules to solve vote percentage and election margin calculations.

  • Identify the base of every percentage: total electorate, votes polled or valid votes.
  • Candidate votes = percentage × total votes ÷ 100.
  • For two candidates, winning margin = percentage-point difference × total valid votes ÷ 100.
  • Total valid votes = numerical margin × 100 ÷ percentage-point difference.
  • Votes polled = total electorate × turnout percentage ÷ 100.
  • Valid votes = votes polled × (100 − invalid percentage) ÷ 100.
  • Candidate percentages based on the same total must add to 100% when all candidates are included.
  • Percentage points and percentage increase are different: 60% − 40% is a 20-percentage-point difference, not a 20% increase.

Election Based Percentage FAQs

What is the vote percentage formula for a candidate?

Candidate votes = (Candidate percentage ÷ 100) × Total votes. For 62% of 15,000 valid votes, the candidate receives 9,300 votes.

How is the winning margin calculated when two candidates receive 53% and 47% votes?

The percentage difference is 6 percentage points. If total valid votes are 30,000, the margin is 6/100 × 30,000 = 1,800 votes.

How do you find total valid votes when the margin is given?

Use Total valid votes = Margin × 100 ÷ percentage-point difference. A margin of 2,000 with a 10-point difference gives 2,000 × 100 ÷ 10 = 20,000 valid votes.

Are turnout percentage and candidate vote percentage calculated on the same base?

Usually, no. Turnout is based on the total electorate, while a candidate’s percentage is commonly based on valid votes. Follow the base stated in the question.

How are invalid votes handled in election percentage questions?

First calculate votes polled, then remove invalid votes. If 25,000 votes are polled and 8% are invalid, valid votes = 25,000 × 92/100 = 23,000.

What does a 15-percentage-point lead mean in an election?

It means the winner’s vote share is 15 percentage points higher than the loser’s share. With 40,000 valid votes, the numerical margin is 15/100 × 40,000 = 6,000 votes.

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