Question
There were two candidates in an election. 20% of the
total voters did not cast their votes. 15% of the total voters’ votes were declared invalid. If the winning candidate received 60% of the valid votes and won by 1040 votes, find the total number of voters.Solution
Let total voters = N Votes cast = 80% of N = 0.80N Invalid votes = 15% of N = 0.15N Valid votes = 0.80N − 0.15N = 0.65N Winner’s votes = 60% of valid = 0.60 × 0.65N = 0.39N Loser’s votes = 40% of valid = 0.40 × 0.65N = 0.26N Winning margin = 0.39N − 0.26N = 0.13N Given margin = 1040 0.13N = 1040 N = 1040 / 0.13 = 8000 Answer: Total number of voters = 8000
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