In an election between two candidates, 65% of the voters cast their votes, out of which 3% of the votes were decided to be invalid. A candidate got 81965 votes which are 65% of the total valid votes. What is the total number of votes enrolled in that election?

200000

Let the total number of votes enrolled be 100x

65% of the voters cast their votes

 Number of votes cast = 100x × \(\frac{ 13}{20}\)

= 65x

invalid votes = 3% . so, valid  votes = 97%

 Number of valid votes = Number of Votes cast x 97%

=  65x × \(\frac{97}{100}\)

= 63.05x

A candidate got 81965 votes which are 65% of the total valid votes

 A candidate gets votes = 65% of total valid votes

 = 63.05x × \(\frac{65}{100}\)

According to the question,

63.05x × \(\frac{65 }{1000000}\) = 81965

x = 2000

100x = 200000

So , total number of total votes = 200000