In an election between two candidates, 64% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 12,288 votes which were 64% of the to... In an election between two candidates, 64% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 12,288 votes which were 64% of the total valid votes. Find the total number of votes enrolled in that election. Read more

Steps to Solve

1. Understand the Variables
   Let the total number of votes enrolled be denoted as ( V ). Given that 64% of voters cast their votes, we can write: $$ \text{Votes cast} = 0.64V $$

2. Calculate Valid Votes
   Out of the votes cast, 4% were declared invalid. Therefore, valid votes can be calculated as: $$ \text{Valid votes} = \text{Votes cast} - \text{Invalid votes} = 0.64V - 0.04(0.64V) $$ This simplifies to: $$ \text{Valid votes} = 0.64V(1 - 0.04) = 0.64V \times 0.96 = 0.6144V $$

3. Relate Candidate Votes to Valid Votes
   It is given that the candidate received 12,288 votes, which were 64% of the total valid votes. We can express this as: $$ \text{Candidate votes} = 0.64 \times \text{Valid votes} $$ Substituting our expression for valid votes: $$ 12,288 = 0.64 \times 0.6144V $$

4. Solve for Total Votes
   Now, we isolate ( V ) by simplifying the equation: $$ 12,288 = 0.393216V $$ Thus, we solve for ( V ): $$ V = \frac{12,288}{0.393216} $$

5. Calculate Total Votes
   Perform the calculation: $$ V \approx 31,250 $$