Question : In an election between two candidates, 80% of the voters cast their votes, out of which 5% votes were declared invalid. A candidate got 9500 votes which were 80% of the valid votes. Find the total number of voters enrolled in that election.
Option 1: 14780
Option 2: 15100
Option 3: 15625
Option 4: 16100
Correct Answer: 15625
Solution :
Let the total number of voters enrolled in the election as V.
From the problem, we know that 80% of the voters cast their votes, so the number of votes cast is 0.8V.
Out of these, 5% of votes were declared invalid, so the number of valid votes is 95% of the votes cast = 0.95 × 0.8V = 0.76V
We also know that a candidate got 9500 votes, which were 80% of the valid votes.
⇒ 0.8 × 0.76V = 9500
$\therefore$ V = 15625
Hence, the correct answer is 15625.
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