Question

In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. 
In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. 
The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election.

	Constituency
	A	B	C	D
No. of candidates contesting	10	12	5	8
Total No. of valid votes polled	5,00,000	3,25,000	6,00,030
No. of votes polled by the winning candidate	2,75,000	48,750
No. of votes polled by the first runner up	95,000			37,500
No. of votes polled by the second runner up				30,000
% of valid votes polled by the third runner up				10%

The following additional facts are known: 
1. The first runner up polled 10,000 more votes than the second runner up in constituency A.
2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.
What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A? [This Question was asked as TITA]

• A. 7%
• B. 9%
• C. 10%
• D. 13%

Answer 1

The Correct Option is B

Constituency A Analysis

Total Valid Votes:

• Constituency A recorded 500,000 total valid votes.

Security Deposit Requirement:

• A candidate requires \( \frac{1}{6} \times 500,000 = 83,334 \) valid votes to retain their security deposit.

Vote Distribution:

• Winner: 275,000 votes.
• 1st runner-up: 95,000 votes.
• 2nd runner-up: 85,000 votes.
• Combined votes for the top three: 275,000 + 95,000 + 85,000 = 455,000 votes.

Remaining Votes:

• Votes for other candidates: 500,000 - 455,000 = 45,000 votes.

Candidates Losing Security Deposit:

• The remaining candidates collectively received 45,000 votes, which is less than the 83,334 votes required per candidate to retain their deposit. Therefore, these candidates forfeited their security deposits.

Percentage of Votes for Candidates Losing Deposit:

• The percentage of total valid votes received by candidates who lost their security deposit is \( \frac{45,000}{500,000} \times 100 = 9\% \).

The final result for constituency A is:

• Candidates who lost their security deposit collectively secured 9% of the total valid votes.

Constituency C Analysis

Information:

• In constituency C, no candidate lost their security deposit.
• The vote difference between any two candidates is a minimum of 10,000 votes.

Vote Distribution:

• The 5th highest vote-getter received more than \( \frac{600,030}{6} = 100,006 \) votes.
• Given the minimum 10,000 vote difference, the vote distribution is as follows:
  • Winner: 140,006 votes.
  • 1st runner-up: 130,006 votes.
  • 2nd runner-up: 120,006 votes.
  • 3rd runner-up: 110,006 votes.
  • 4th runner-up: 100,006 votes.
• The sum of votes for these top five candidates is 600,030.

Constituency D Analysis

1. Information:
   • Constituency D has a total of 100x votes.
   • The winning candidate received 15𝑥+37,500 votes.

Updated Table Summary

The following table summarizes the provided information:

Constituency	Total Votes	Winner Votes	1st Runner-Up Votes	2nd Runner-Up Votes	3rd Runner-Up Votes	4th Runner-Up Votes	5th Highest Votes	Total of Top 5 Votes
A	500,000	275,000	95,000	85,000	-	-	-	455,000
C	600,030	140,006	130,006	120,006	110,006	100,006	>100,006	600,030
D	100x	15x+37,500	-	-	-	-	-	-

Conclusion:

• Constituency A: Candidates who forfeited their security deposits accounted for 9% of the total votes.
• Constituency C: The vote distribution is detailed in the table, ensuring all candidates met the threshold to retain their security deposits.
• Constituency D: Additional information is required for a complete analysis.

This table provides a concise overview of the vote distribution and calculations for each constituency based on the provided data.
The correct answer is option (B): 9%