Final answer:
The number of voters enrolled on the voters list is approximately 64285.71.
Step-by-step explanation:
To find the number of voters enrolled on the voters list, we need to calculate the valid votes first. Let's assume the total number of voters enrolled on the voters list is 'x'.
10% of voters did not cast their vote, which means 90% of the total voters cast their vote. Therefore, the number of voters who cast their vote is 90% of 'x', which is 0.9x.
10% of the votes polled were invalid. So, the number of valid votes is 90% of 0.9x, which is 0.81x.
The successful candidate got 54% of the valid votes. Therefore, the number of valid votes for the successful candidate is 54% of 0.81x, which is 0.4374x.
The successful candidate won by a majority of 1620 votes. This means the number of votes received by the successful candidate is 1620 more than the number of votes received by the other candidate.
Therefore, 0.4374x - (0.9x - 0.4374x) = 1620
Simplifying the equation, we get 0.4374x - 0.9x + 0.4374x = 1620
Combining like terms, we get 0.4374x - 0.4626x = 1620
Simplifying further, we get -0.0252x = 1620
Dividing both sides of the equation by -0.0252, we get x = 1620 / -0.0252
Calculating the value of x, we get x ≈ 64285.71
Therefore, the number of voters enrolled on the voters list is approximately 64285.71.