In an election, only two candidates contested. One candidate secured 70% of the valid votes and won by a major

Question

In an election, only two candidates contested. One candidate secured 70% of the valid votes and won by a majority of 172 votes. The total number of valid votes was:

Examoogle · Accepted Answer

The correct answer is Option C: 430. Finding Total Valid Votes from Winner's Percentage and Majority

Step-by-Step Solution & Concepts:
Key Fact: Finding Total Valid Votes from Winner's Percentage and Majority

Given: Winner secured $70\%$ of valid votes; Winning margin = $172	ext{ votes}$

Key Formulas: $	ext{Valid Votes} = \frac{	ext{Majority Margin}}{\%_1 - \%_2} 	imes 100$

Key Points: Winner received $0.70 	imes 430 = 301$ votes.; Loser received $0.30 	imes 430 = 129$ votes.; $301 - 129 = 172$ votes.

Steps: Find the Percentage Margin: Since only two candidates contested: $$	ext{Loser's Share} = 100\% - 70\% = 30\%$$ $$	ext{Difference (Majority)} = 70\% - 30\% = 40\%	ext{ of valid votes}$$. Compute Total Valid Votes: $$40\% 	imes V = 172$$ $$V = \frac{172}{40} 	imes 100 = 4.3 	imes 100 = 430$$

Answer: Option C is correct — 430

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