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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.

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:

The first runner up polled 10,000 more votes than the second runner up in constituency A.

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.

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?

Entered answer:

✅ Correct Answer: 9

Slide 1/6

Understanding the set :-

There is an election held at four constituency - A, B, C, D

There is an half-filled table in the set which gives information about, number of candidates, valid votes, etc.

Also, 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.

A candidate is defeated if he/she was unable to secure even 1/6th of the votes polled.

(Defeating candidates are all the candidates who is not a winner - even first, second runner up are defeating candidates).

This is a table set,

In this set you are just required to fill the table given in the set, using clues given at the end.

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
Votes polled by winning candidate	2,75,000	48,750
Votes polled by first runner-up	95,000			37,500
Votes polled by second runner-up	85,000			30,000
% votes polled by third runner-up				10%
Total votes of remaining candidates	45000

Clue 1 says,

The first runner up polled 10,000 more votes than the second runner up in constituency A.

=> Second runner up's votes polled = $95000 - 10000 = 85000$

Nwo, we know total number of candidates in A = 10

Therefore, votes of remainng 7 = $500000 - 275000- 95000 - 85000 = 45000$

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
Votes polled by winning candidate	2,75,000	48,750	1,40,006
Votes polled by first runner-up	95,000		1,30,006	37,500
Votes polled by second runner-up	85,000		1,20,006	30,000
% votes polled by third runner-up			(1,10,006)	10%
Total votes of remaining candidates	45000		1,00,006

Clue 2 says,

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.

Now, we know, 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.

=> In constituency C all candidates have secured more than 1/6th of total valid votes.

=> $\dfrac{1}{6}\times6,00,030 = 1,00,005$

Also, we know, difference in votes polled by any pair of candidates in this constituency was at least 10,000.

If difference in votes is exactly 10000, then

4th runner up will have more then 1,00,005 let that be = $1,00,006$ votes

=> 3rd runner up = $1,00,006 + 10000 = 1,10,006$

=> 2nd runner up = $1,10,006 + 10000 = 1,20,006$

=> 1st runner up - $1,20,006 + 10000 = 1,30,006$

and, Winner = $1,40,006$

Noe the total of all = $1,00,006 + 1,10,006 + 1,20,006 + 1,30,006 + 1,40,006 = 6,00,030$

which is equal to total number of votes polled in constituency C.

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	x
Votes polled by winning candidate	2,75,000	48,750	1,40,006	37,500 + 5x
Votes polled by first runner-up	95,000		1,30,006	37,500
Votes polled by second runner-up	85,000		1,20,006	30,000
% votes polled by third runner-up			(1,10,006)	10%
Total votes of remaining candidates	45000		1,00,006

Clue 3 says,

The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up.

Let the total valid votes be '100x'

Also, We know, votes polled by first runner up in constituency D is $37,500$

=> Winner candidates polled = $37,500 + 5x$

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	1,75,000
Votes polled by winning candidate	2,75,000	48,750	1,40,006	72,500
Votes polled by first runner-up	95,000		1,30,006	37,500
Votes polled by second runner-up	85,000		1,20,006	30,000
% votes polled by third runner-up			(1,10,006)	10%
Total votes of remaining candidates	45000		1,00,006

Continuing with clue 3,

All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.

=> the candidates who got security deposit must have got 65% of votes.

We can make two cases:

Case I: Let top three candidates got the security deposit

=> $37500+5x+37500+30000 =65x$

=> x= $1750$

=> $100x= 175000$

Case II: Let top three candidates got the security deposit

=> $37500+5x+37500 =65x$

=> $60x = 1250$

=> $x = 125000$

but 1/6th of of 125000 = 20834

=> 2nd runner up must got security deposit.

So, this case is not valid.

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	1,75,000
Votes polled by winning candidate	2,75,000	48,750	1,40,006	72,500
Votes polled by first runner-up	95,000		1,30,006	37,500
Votes polled by second runner-up	85,000		1,20,006	30,000
% votes polled by third runner-up			(1,10,006)	10%
Total votes of remaining candidates	45000		1,00,006

Votes got by Second runner up from A= 95000-10000= 85000

Votes got by the candidates who lost their security deposits= 500000-275000-95000-85000= 45000

Required % = $\frac{45000}{500000}\times100 = 9\%$

So answer is option 1

Question 12

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

Question 13

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

Question 14

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

Question 15

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?

Question 16

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?

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

Solution

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