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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.
|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%|
Question 13 : What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?
Let's try to fill the table first. Partially applying points 1 and 3 we can get the votes for the 2nd runner up in A and the winning candidate in D.
To begin answering this question, we need to first see what is the% of total votes between the candidates we already know about: Winner + 1st + 2nd Runner Up total: 455,000 (91%)
So the vote share among the remaining 7 candidates was only 9%
To lose security deposit, one must get less than or equal to 1/6th i.e. lesser than 16.67% of the total votes. Clearly that is indeed the case with the remaining candidates in A.
The question is "What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?"
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