In a state election between two parties, 83% of the voters cast their votes, out of which 4% of the votes were declared invalid. Party A got 156611 votes which were 83% of the total valid votes. Find the total number of votes enrolled in that election. (Consider integer part only)

The correct option is 2,36,807.

Let the total number of enrolled voters in the election be $X$.

Step 1: Calculate the total number of votes cast
It is given that 83% of the enrolled voters cast their votes.
$\text{Total votes cast}=83\%\text{of}X=\frac{83}{100}\times X$

Step 2: Calculate the number of valid votes
Out of the total votes cast, 4% were declared invalid. This means that 96% of the votes cast were valid.
$\text{Total valid votes}=96\%\text{of}(\frac{83}{100}\times X)=\frac{96}{100}\times \frac{83}{100}\times X$

Step 3: Set up the equation using the votes obtained by Party A
Party A received 156611 votes, which represents 83% of the total valid votes.
$83\%\text{of}\text{Total valid votes}=156611$
$\frac{83}{100}\times (\frac{96}{100}\times \frac{83}{100}\times X)=156611$

Step 4: Solve for $X$
$X=\frac{156611\times 100\times 100\times 100}{83\times 96\times 83}$

First, divide 156611 by 83:
$156611÷83=1886.8795$

Dividing by 83 again:
$1886.8795÷83=22.733488$

Now, multiply by 1,000,000 and divide by 96:
$X=\frac{22733488}{96}\approx 236807.16$

Taking only the integer part, the total number of votes enrolled in the election is 2,36,807.