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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