In an election between two candidates, 10% of the voters did not cast their votes and 5% of the votes polled were found invalid. The successful candidate got 52.5% of the valid votes and won by a majority of 1710 votes. The number of voters enrolled on the voters list was:

Correct option is B

Given:
People who did not cast their votes= 10%
Polled votes which were invalid = 5%
Successful candidate secured = 52.5%
Successful candidate won by = 1710 votes
Solution:

Let the total valid votes be 100%
Successful candidate secured = 52.5%
Other candidate secured = 100-52.5%= 47.5%
Difference of vote percentage = 52.5-47.5 = 5%
5%= 1710
1%= $$\frac{1710}{5}$$​​
100%= $$\frac{1710}{5}$$​ ×100= 34200
Invalid votes = 5%
Valid votes =100-5 = 95%=34200
95%=34200
1%=$$\frac{34200}{95}$$​​

100%=$$\frac{34200}{95}$$​×100= 36000
People who did not cast their votes =10%
People who cast their votes =100-10 =90%=36000
90%= 36000
1%= $$\frac{36000}{90}$$​​
100%= $$\frac{36000}{90}$$​ ×100= 40000

Alternate Method:

Let the total number of voters be x .
10% of the voters did not vote:
=> Voters who voted = x - 0.10x = 0.90x
5% of the votes polled were invalid, Invalid votes = 0.05 × 0.90x = 0.045x
=> Valid votes = 0.90x - 0.045x = 0.855x
=> Votes received by successful candidate = 0.525 × 0.855x = 0.448875x
Let the votes received by the other candidate be q.
=> Total valid votes = Votes received by successful candidate + Votes received by the other candidate
=> 0.855x = 0.448875x + q
=> q = 0.855x - 0.448875x = 0.406125x
The majority is 1710 votes:
=> 0.448875x - 0.406125x = 1710
=> 0.04275x = 1710
=> x = 40000