Numerical answer
In an election between two candidates, 10% of the voters on the voters' list did not vote and 60 votes cast were declared invalid. The winning candidate received votes equal to 47% of the total number of voters on the list and won by a margin of 1,200 votes. How many voters were there on the list?
Show answer and solution
Answer: 28500
Let the number of voters on the list be N.
Votes cast = 0.9N; valid votes = 0.9N − 60.
Winner = 0.47N; loser = (0.9N − 60) − 0.47N = 0.43N − 60.
Margin = 0.47N − (0.43N − 60) = 0.04N + 60 = 1200.
0.04N = 1140 → N = 28,500.
Trap: The 47% is of the total list, not of valid votes; mixing bases gives wrong answers.
Votes cast = 0.9N; valid votes = 0.9N − 60.
Winner = 0.47N; loser = (0.9N − 60) − 0.47N = 0.43N − 60.
Margin = 0.47N − (0.43N − 60) = 0.04N + 60 = 1200.
0.04N = 1140 → N = 28,500.
Trap: The 47% is of the total list, not of valid votes; mixing bases gives wrong answers.
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