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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.

  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.

Question 17 : The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

  1. B, D, C, A 
  2. D, B, C, A
  3. D, C, B, A  
  4. B, C, D, A

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Explanatory Answer

A clearly has the highest margin
With B, margin could be as low as possible since everyone lost their deposit. Highest could be as follows: assume that the first 11 people got 1 - 11 votes only (since there are no ties, we are increasing the numbers by 1 for each position). So the winning margin can be as high as ~48,000
C it is 10,000 as calculated earlier
D is less than 10,000 for sure since it is 5% of the valid votes

So D cannot be more than C. The only option which has D more than C is the last one

The answer is, "B, C, D, A"

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