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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 15 : What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

  1. between 1,40,005 and 1,40,010
  2. 1,40,006 
  3. less than 2,00,010
  4. 1,40,010

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Explanatory Answer

It is mentioned that none in C lost their security deposit and the delta in votes was at least 10,000

The least possible vote share is slightly more than 1/6th, meaning the lowest possible value here is: 600,030 / 6 +1 = 100,005 + 1. If noone lost the security deposit, then the least possible value is 100,006
Assuming a 100,00 vote delta just for the time being we get the following as our possible values

Unfinished table

Clearly given the constraints, there isn't too much we can do to flex the numbers here.This is the only possible way to satisfy the constraints. So this must be the answer.

The question is "What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?"

Hence, the answer is, "1,40,006 "

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