Percentage

Starting from the back. If the successful candidate got 54% of the votes, the other guy got 46% (since there are only two candidates). So we see a difference of 8% yields a difference of 1620 people. So the total number of valid votes is 1620 100/8=20250 And only 90% of votes cast were valid. So number of votes cast was 20250 100/90=22500

And only 90% of registered voters voted. So total number of voters=22500*10/9=25000.

let the no. of voters be =x 10% ie 1/10 of x non voters therefore no.of voters= 9/10.x 10% of 9x/10 = invalid votes therefore 9x/10-9x/100= 81x/100 =valid votes winning candidate got 54% = 54/100 of 81x/100 therefore losing candidate got= 46/100 of 81x/100 the winning difference = 1620 solving for 54/100 of 81x/100 - 46/100 of 81x/100=1620 = 81x(54-46)=1620 10000 x= 1620 10000/81*8 x= 20.1250 x= 25000 no. of voters on the voting list =25000

let x = number of valid votes. 0.54x - 0.46x = 1620 (The Majority) ==> x = 20250

Then, let y = number of votes polled. Since there 10% of votes polled were invalid, 0.9y = x = 20250 (The Valid Votes) ==> y = 22500

Lastly, let z = number of voters. As there were 10% of voters didn't cast their votes, 0.9z = y = 22500 (The Votes Polled) ==> z = 25000

Solution: There are 25000 of votes enrolled.