Question

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

• A. 40192
• B. 60288
• C. 50240
• D. 62800

Answer 1

The Correct Option is D

Given: 
- 30% of the voters voted,
- 80% of those who voted supported the first candidate.

Step 1: Percentage of total voters who voted for the first candidate
\(0.30 \times 0.80 = 0.24 = 24\%\)

Step 2: Remaining votes out of total voters
Total votes cast = 30% of all voters
Votes for first candidate = 24%
Therefore, remaining = \(30\% - 24\% = 6\%\) of total voters
But we are told the remaining votes (not the remaining among voters, but among all votes) are 80% - 24% = \(56\%\).

This 56% is the total votes received by the remaining candidates.
These votes were distributed in the ratio 3:2:1.

Step 3: Fourth candidate's share out of remaining votes
Total parts in the ratio = \(3 + 2 + 1 = 6\)
Fourth candidate's share = \(\frac{3}{6} = \frac{1}{2}\) of 56%
\(\frac{1}{2} \times 56\% = 28\%\)

Step 4: Find the difference between the winner and runner-up
- First candidate received = \(24\%\)
- Fourth candidate received = \(28\%\)
- Difference = \(28\% - 24\% = 4\%\)

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

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