In an election between two candidates, one got 55% of the total valid votes and 20% of the votes were invalid.

Question

In an election between two candidates, one got 55% of the total valid votes and 20% of the votes were invalid. If the total number of votes was 7500, then the winner won the election by a majority of ________ votes.

Examoogle · Accepted Answer

The correct answer is Option C: 600. Calculating Winning Majority in an Election with Invalid Votes

Step-by-Step Solution & Concepts:
Key Fact: Calculating Winning Majority in an Election with Invalid Votes

Given: Total votes = $7,500$; Invalid votes = $20\%$; Winner's share = $55\%$ of valid votes

Key Formulas: $	ext{Majority} = (\%_1 - \%_2) 	imes 	ext{Valid Votes}$

Key Points: Winner got 3,300 votes; Loser got 2,700 votes.; Difference = 600 votes.

Steps: Calculate Total Valid Votes: $$	ext{Valid Votes} = 7500 	imes (100\% - 20\%) = 7500 	imes 0.80 = 6,000$$. Determine Vote Margin (Majority): Winner received $55\%$ of valid votes, meaning the other candidate received $100\% - 55\% = 45\%$. $$	ext{Majority } \% = 55\% - 45\% = 10\%	ext{ of valid votes}$$ $$	ext{Majority} = 10\% 	imes 6000 = 600	ext{ votes}$$

Answer: Option C is correct — 600

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