Question:hard

In an election,there were four candidates and \(80\%\) of the registered voters casted their votes.One of the candidates received \(30\%\) of the casted votes while the other three candidates received the remaining casted votes in the proportion \(1\ratio2\ratio3\).If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

Updated On: Jan 15, 2026

  • 40192

  • 60288

  • 50240

  • 62800

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The Correct Option is D

Solution and Explanation

Provided Information:
- 30% of the electorate participated in the vote.
- Of those who voted, 80% favored the leading candidate.

Step 1: Calculate the leading candidate's percentage of total electorate
\(0.30 \times 0.80 = 0.24 = 24\%\)

Step 2: Determine the percentage of total electorate for remaining candidates
Percentage of electorate who voted = 30%
Percentage of electorate who voted for the first candidate = 24%
Percentage of electorate who did not vote for the first candidate =\(30\% - 24\% = 6\%\) of the total electorate.
However, the remaining votes constitute 56% of the total electorate, calculated as the difference between the votes for the first candidate and the total votes cast by the remaining candidates who received 80% of the votes cast. (Note: The original text has a discrepancy here. Assuming the 80% refers to the votes cast and the calculation 80% - 24% = 56% represents the share of votes for other candidates from the total electorate.)

These 56% of votes were distributed among the remaining candidates in a 3:2:1 ratio.

Step 3: Calculate the fourth candidate's share of the total electorate
Total ratio parts =\(3 + 2 + 1 = 6\)
The fourth candidate's share represents 3 parts of the ratio.
Fourth candidate's share =\(\frac{3}{6} = \frac{1}{2}\) of the 56% of total electorate.
\(\frac{1}{2} \times 56\% = 28\%\)

Step 4: Calculate the difference in votes between the winner and runner-up
- Leading candidate's share =\(24\%\)
- Fourth candidate's share =\(28\%\)
- Difference =\(28\% - 24\% = 4\%\)

Step 5: Calculate the total number of voters
Given: \(4\% = 2512\)
Therefore, \(1\% = \frac{2512}{4} = 628\)
Total voters (100%) =\(628 \times 100 = 62800\)

Final Result: Total number of voters =\(62800\)

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