DIRECTIONS for the question: Go through the graph and the information given below and answer the question that follows.
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:
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.
EXPLAINATION:
As it is given in the question that the first runnerup polled 10,000 more votes than the second runnerup in constituency A. Now the first runnerup has got 95000 votes, hence the second runnerup will get 85000 votes. Therefore the remaining votes will be 500000  275000  95000  85000 = 45000
As per the second additional point given, 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 person who got the 5th highest votes must have got greater than 600030/6 = 100006. As it is also given that the difference of votes is greater than 10000, the only possible case is winner, 1st runner up, 2nd runner up, 3rd runner up, 4th runner up must have got 140006,130006,120006,110006,100006 respectively which sums up to exactly 600030.
Let the number of votes polled in D be 100x.
From 3, The winning candidate in constituency D must have got 15x + 37500 The table now looks like this:

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 
100x 
No. of votes polled by the winning candidate 
2,75,000

48,750 
140006 
(37500 + 100x) 
No. of votes polled by the first runner up 
95,000 

130006 
37,500 
No. of votes polled by the second runner up 
85000 

120006 
30,000 
% of valid votes polled by the third runner up 


16.67% 
10% 
The candidates who didn't lose the deposit must have got less than 16.67% ⇒ 3rd runnerup must surely didn't get the deposit.
Also, the candidates who got security deposit must have got 65% of the votes.
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 16.66% of 125000 = 20834 ⇒ 2nd runner up must got security deposit. So, this case is not valid.
For all the constituencies let's look at the candidates who lost their security deposit.
A (500000  275000  95000  85000) = 45000.
B (325000  48750) = 276250
C (0) and D (61250) = 175000  46250  30000  37500
Hence percentage will be 382500/1600000x100 = 23.91%