We know that candidates who failed to secure more 1/6 th of total valid votes lose their
security deposit.
Let us put the information we have in a table:
• From (1), we know that the 2 nd runner-up in A polled 95000-10000 = 85000 votes
• From (2), we know that everyone in C secured more than (1/ 6)* 600030 = 100005 votes . Also,
the minimum difference between any 2 candidates’ votes was 10,000.
• From (3), let’s assume the total no. of votes polled in D was 100x. Then votes polled by winner =
37,500 + 5x.
Also, we know that candidates who lost their deposit in D together polled 35% votes . 

Total votes polled in D = 100x
Votes secured by top 4 = 37,500 + 5x + 37,500 + 30,000 + 10x = 1,05,000 + 15x
We can also see that the 3 rd runner-up secured less than 1/6 th (10%) votes and hence lost
security deposit. So, minimum 5 and maximum 7 candidates lost security deposit.
We can have 3 cases here:
CASE I: 7 candidates (all except winner) lost security deposit. In this case, top candidate will
have remining 65% votes.
37,500 + 5x = 65x
60x = 37,500
x = 625
Total votes polled = 100x = 62 , 500
1/6 th of 62,500 = 10,417
Votes secured by 1 st runner-up = 37,500 > 10,417
1 st runner up couldn’t have lost deposit. Hence, this case is not feasible.

CASE II: 6 candidates (all except winner & 1 st runner-up) lost security deposit. In this case, top 2
candidates will have remining 65% votes.
37,500 + 5x + 37,500 = 65x
75,000 = 60x
x = 1250
Total votes polled = 100x = 1,25,000
1/6 th of 1,25,000 = 20,833 
Once again, 1 st runner-up secured more than 1/6 th votes and couldn’t have lost deposit. This
case is also not feasible.
CASE III: 5 candidates (all except winner, 1 st runner-up & 2 nd runner-up) lost security deposit.
In this case, top 3 candidates will have remining 65% votes.
75,000 + 5x + 30,000 = 65x
60x = 1,05,000
x = 17 50
Total votes polled = 100x = 1,75,000
1/6 th of 1,75,000 = 29,167
Votes secured by 3 rd runner-up = 10x = 10,500 < 29,167
Hence, this is the only feasible case.
Therefore, total number of valid votes polled in D is 1,75,000.