Question : In an election between two candidates, 65% of the voters cast their votes, out of which 3% of the votes were decided to be invalid. A candidate got 81,965 votes, which is 65% of the total valid votes. What is the total number of votes enrolled in that election?
Option 1: 2,00,000
Option 2: 1,90,000
Option 3: 2,15,000
Option 4: 1,85,000
Correct Answer: 2,00,000
Solution :
Let the total number of voters registered be $x$.
65% of the voters cast their votes.
Casted votes = $\frac{65x}{100}$
3% of cast votes were declared invalid.
Valid votes = $\frac{97}{100}×\frac{65x}{100}$
A candidate got 81965 votes which are 65% of the total valid votes.
So, $\frac{97}{100}×\frac{65x}{100}×\frac{65}{100}=81965$
$⇒x=\frac{81965×100×100×100}{65×65×97}$
$\therefore x = 200000$
Hence, the correct answer is 2,00,000.
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