In an election between two candidates, 10% of the voters did not cast their votes and 75 votes were found invalid. The winner got 50% of the total votes expected and won by 170 votes. How many voters were enrolled in the voters’ list?

The correct option is 950.

Let us solve the problem step-by-step by defining the variables and setting up the equations based on the information provided in the question.

Let the total number of voters enrolled in the voters' list be represented by $x$.

According to the problem, 10% of the enrolled voters did not cast their votes. Therefore, the number of voters who cast their votes is:
$100\%-10\%=90\%\text{ of }x=0.9x$

From the votes cast, 75 votes were found to be invalid. Thus, the total number of valid votes is:
$\text{Valid Votes}=0.9x-75$

We are given that the winner got 50% of the total votes expected (which refers to the total number of enrolled voters, $x$). Therefore, the number of votes obtained by the winner is:
$\text{Winner's Votes}=50\%\text{ of }x=0.5x$

The remaining valid votes were obtained by the loser. Thus, the number of votes obtained by the loser is:
$\text{Loser's Votes}=\text{Total Valid Votes}-\text{Winner's Votes}$
$\text{Loser's Votes}=(0.9x-75)-0.5x=0.4x-75$

The winner won by 170 votes, which means the difference between the winner's votes and the loser's votes is 170:
$\text{Winner's Votes}-\text{Loser's Votes}=170$

Substituting the expressions we found:
$0.5x-(0.4x-75)=170$

Simplify the equation by distributing the negative sign:
$0.5x-0.4x+75=170$
$0.1x+75=170$

Subtract 75 from both sides of the equation:
$0.1x=170-75$
$0.1x=95$

Divide by 0.1 to find the value of $x$:
$x=\frac{95}{0.1}=950$

Therefore, the total number of voters enrolled in the voters' list was 950.