Data Interpretation – In an election several candidates contested for a constituency

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.

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.

Q.1 What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?

Answer: 9

Q.2 How many candidates who contested in constituency B lost their security deposit?

Answer: 11

Q.3 What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

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

Answer: 3

Q.4 What was the number of valid votes polled in constituency D?

1. 1,50,000
2. 1,75,000
3. 62,500
4. 1,25,000

Answer: 2

Q.5 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, C, D, A
2. B, D, C, A
3. D, C, B, A
4. D, B, C, A

Answer: 1

Q.6 For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?

1. 38.25%
2. 23.91%
3. 32.00%
4. 23.54%

Answer: 2

Solutions:
Q.1 No of votes polled by 2nd runner up = 95000 – 10000 = 85000
Total votes polled for winner , first runner up and 2nd runner up = 275000+95000+85000 = 455000
Remaining votes = 500000 – 455000 = 45000
45000 is combined votes of remaining 7 candidates which is less than 1/6 th of total votes polled so they will loss their security deposite .
Thus required %tage = 45000/500000 *100 = 9%
Answer :9

Q.2 Total votes polled = 325000
1/6th of total votes = 325000/6 = 54166.66
And it is given that the winner scored 48750 votes which mean all the other candidates get less than 48750 votes that is less than 1/6th of total votes polled so they all will lose their security deposite.
Thus required answer = 12 -1 =11

Q.3 Minimum votes for the last candidate = 600030/6 = 100006
Minimum votes for the 2nd last candidate = 110006
Minimum votes for the 3rd last candidate = 120006
Minimum votes for the 4th last candidate = 130006
Minimum votes for the 5th last (winner) candidate = 140006
Sum = 600030
Thus required answer 4) 140,006

Q.4 Let the total valid votes polled = 100x
Then votes polled for winner = 37500 + 5% of 100x = 37500+5x
Thus as per question , 37500+30000+37500 +5x = 100x – 35x
105000 = 60x
x = 105000/60= 1750
so total number of votes polled = 1750*100 = 175000

Q.5 Winning margin in D = 5% of 175000 = 8750
Winning margin in C > 10000
So in increasing order the order of C and D should be D , C not C, D option 3) B, C, D, A
Q.6 Total valid votes = 500000+325000+600030 + 175000 = 1600030
Total number of votes polled for the candidates who lost their security deposit = 45000+(325000 – 48750) + 35% of 175000 = 382500
Required percentage = 382500/1600030 *100 = 23.905% = 23.91%

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