In a two-candidate election, 10% of the voters did not cast their ballots. 10% of the votes cast were found invalid. The winning candidate received 54% of the valid votes and a 1620-vote majority. Find the number of people on the voter list who have registered to vote.

Answer: Option A

Given
10% of the voters did not cast their vote and 10% of the polled vote were found invalid
The winner candidate got 54% of the valid vote and beat the opposition by 1620 votes
Concept used:
The percentage is calculated as based on 100 i.e. 100 is the base
40% means 40 out of 100
Calculation:
Let, total enrolled voter be $$x$$
10% did not cast vote means casted or polled vote = $$\frac{9x}{10}$$
10% vote is invalid
That means valid vote = $$\frac{90}{100}\times \frac{9x}{10}$$
$$\Rightarrow \frac{81x}{100}$$
The winner candidate got 54% of the polled vote means loosed got (100 - 54) = 46% vote
Winner candidate got total $$\left(\frac{54}{100}\times \frac{81x}{100}\right)$$   vote
And the looser candidate got $$\left(\frac{46}{100}\times \frac{81x}{100}\right)$$   vote
Accordingly,
$$\begin{array}{rl}& \left(\frac{54}{100}\times \frac{81x}{100}\right)-\left(\frac{46}{100}\times \frac{81x}{100}\right)=1620\\ & \Rightarrow \left(\frac{81x}{100}\right)\times \left(\frac{54-46}{100}\right)=1620\\ & \Rightarrow \frac{\left(81\times 8\right)x}{10000}=1620\\ & \Rightarrow x=\frac{1620\times 10000}{81\times 8}\\ & \Rightarrow x=25000\end{array}$$
∴ Total 25000 voters registered in the voter list.