CAT Problems based on election - Practice Questions & MCQ

Elections play a significant role in a democratic society.

Problems based on election are frequently asked in management entrance exams.

These problems test your understanding of concepts like percentages, ratios, and fractions.

Basic Concepts

Understanding percentages: A percentage is a fraction whose denominator is always 100.

Convert percentages to fractions: Divide the given number by 100 and simplify if possible.

Convert fractions to percentages: Multiply the given fraction by 100.

Relation between fractions, decimals, and percentages: Fractions and decimals can be directly converted into percentages.

Types of Problems in Election-based Questions

Type 1: Total Votes, Valid Votes & Invalid Votes

Formulae:

1. Total Votes = Valid Votes + Invalid Votes

2. Percentage of Valid Votes = 

3. Percentage of Invalid Votes = 

Example:

In an election between two candidates, 10% of the votes were declared invalid. If the total number of votes was 2000, how many valid votes were cast?

Solution: 

Using the second formula:

Invalid Votes = 10% of 2000 = 200

Valid Votes = 2000 - 200 = 1800

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Type 2: Majority & Margin

Formulae:

1. Majority or Winning Margin = Votes secured by Winning Candidate - Votes secured by Losing Candidate

Example:

In an election between A and B, A secured 55% of the valid votes and won by a majority of 200 votes. Find the total valid votes.

Solution:

Let the total valid votes be (x).

Votes secured by A = 0.55x

Votes secured by B = x - 0.55x = 0.45x

Given, 0.55x - 0.45x = 200

=> 0.1x = 200

=> x = 2000

Total valid votes = 2000.

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Type 3: Unpolled Votes

Sometimes, not all eligible voters vote in an election. The difference between total eligible voters and those who actually voted is termed as "unpolled votes".

Formulae:

1. Unpolled Votes = Total eligible voters - Total Votes

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Tips and Tricks for Problems Based on Election:

1. Read Carefully: Sometimes the problem gives information on the percentage of votes a candidate got out of the total votes, and sometimes out of the valid votes. Always read the question carefully to determine which it is.

2. Work with Ratios: If the exact numbers aren't given, try converting the percentages into ratios. This makes calculations easier and quicker.

3. Use Elimination: If you can't determine the votes of one candidate but have the total and the votes of the other candidates, subtract to find the missing votes.

4. Sketch: Draw a pie chart or bar graph for visualization if you're getting confused with too many percentages. It often simplifies understanding.

5. Practice: Like all quantitative topics, the more you practise, the more patterns you'll recognize, and the quicker you'll solve problems.