Question : In a two-candidate election, 10% of the voters did not cast their ballots. 10% of the votes cast were found invalid. The winning candidate received 54% of the valid votes and a 1620 vote majority. Find the number of people on the voter list who have registered to vote.
Option 1: 25000
Option 2: 26000
Option 3: 24500
Option 4: 25500
Correct Answer: 25000
Solution :
Let $x$ be the total votes.
Voters did not cast their ballots = 10% of $x$
Voters casted their votes = 90% of $x$ = $\frac{9x}{10}$
Invalid votes = 10% of $\frac{9x}{10}$
Valid votes = 90% of $\frac{9x}{10}$ = $\frac{81x}{100}$
Votes of winning candidate = 54% of $\frac{81x}{100}$
Votes of failed candidate = 46% of $\frac{81x}{100}$
Majority = 1620
Now, (54 – 46)% i.e., 8% of $\frac{81x}{100}$ = 1620
$\therefore x$ = $\frac{1620×100×100}{81×8}$ = 25000
Hence, the correct answer is 25000.
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