Question

In an election only two candidates contested, 30% of the registered voters did not cast their votes and 180 voters were declared invalid. The winner got 684 votes more than his opponent and numbers of valid votes received by the winner is 42% of the number of registered voters. ​How many reggistered voters cast theri votes?

Answer 1

let the total registered voters be x

given that 30% did not cast their votes =0.3 x.
so therefore no of voters who cast the votes = x-0.3 x = 0.7 x

so given that no of winner got ,W= Looser + 684

so therefore , W-L=684 

Also given winner votes is 42% of registered voters,W = 0.42 x

NO OF INVALID VOTES= 180


nof cast votes,  0.7 x = W+L+Invalid votes
0.7x= L+684+L+180
0.7X = 2L+864
0.7x=2(0.42x-684)+864     (solve this equation)
0.14x= 504
x= 3600

no of registerd voters= 3600

Answer 2

As the electorate expanded, the political parties evolved to mobilize the growing mass of voters as the means of political control. ... In recent decades, increasing numbers of individual voters classify themselves as “independent,” and they are permitted to register to vote as such in many states.