Question : In an election contested between two candidates, 15% of the total voters did not cast their votes and 100 votes got disqualified. The candidate who won the election won by securing 45% of the total votes and won by a margin of 400 votes. Find the total number of voters.
Option 1: 6,000
Option 2: 3,600
Option 3: 10,000
Option 4: 3,500
Correct Answer: 6,000
Solution :
Let total voters be $x$
Votes that got disqualified $= 100$
Percentage of votes for winner = 45%
The margin between the winner and loser = 400 votes
Total votes cast = Total voters – voters who did not cast votes – Number of votes disqualified
= 100% of $x$ – 15% of $x$ – 100
= 85% of $x$ – 100
Now, votes won by winner = 45% of $x$
So, votes won by loser = 45% of $x$ – 400
According to the question,
Total votes counted = Number of votes for winner + Number of votes for loser
or, 85% of $x$ – 100 = 45% of $x$ + 45% of $x$ – 400
or, 300 = 90% of $x$ – 85% of $x$
or, 300 = 5% of $x$
or, 300 = $\frac{5}{100}x$
or, $x$ = 6000
Hence, the correct answer is 6,000.
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