In an election, 2% persons enrolled in the voter list did not participate and 500 votes were invalid. Two candidates A and B fought the election, and A defeated B by 200 votes. If 43% of the persons enrolled in the voter list casted their votes in favour of A, then what is the number of the total casted votes?

Let the total number of enrolled voters be ( x ).

According to the problem:

– 2% of enrolled voters did not participate, which means 98% did participate.

– The number of valid votes cast would then be ( 0.98x – 500 ) (where 500 is the invalid votes).

– A received 43% of the votes, so A’s votes are ( 0.43 times (0.98x) ).

– B’s votes can then be calculated since A defeated B by 200 votes, which gives us the equation:

( text{Votes for A} = text{Votes for B} + 200 ).

We have:

[

text{Votes for A} = 0.43 times (0.98x)

]

[

text{Votes for B} = (0.98x – 500) – text{Votes for A}

]

Substituting B’s votes into A’s winning margin:

[
0.43 times (0.98x) = (0.98x – 500) – (0.43 times (0.98x)) + 200

]

Simplifying:

[
0.43 times (0.98x) + 0.43 times (0.98x) = 0.98x – 500 + 200

]

[
0.