Numerical answer
In an election between two candidates, 10% of the voters on the list did not cast their vote and 60 of the votes cast were declared invalid. The winning candidate received votes equal to 47% of all the voters on the list and won by a margin of 1,380 votes. How many voters were on the list?
Show answer and solution
Answer: 33000
Let the number of voters on the list be N.
Votes cast = 0.9N; valid votes = 0.9N − 60.
Winner = 0.47N, so loser = 0.9N − 60 − 0.47N = 0.43N − 60.
Margin = 0.47N − (0.43N − 60) = 0.04N + 60 = 1380, giving 0.04N = 1320 and N = 33,000.
Trap: The 47% is of the list, not of the valid votes — read the base of every percentage carefully.
Votes cast = 0.9N; valid votes = 0.9N − 60.
Winner = 0.47N, so loser = 0.9N − 60 − 0.47N = 0.43N − 60.
Margin = 0.47N − (0.43N − 60) = 0.04N + 60 = 1380, giving 0.04N = 1320 and N = 33,000.
Trap: The 47% is of the list, not of the valid votes — read the base of every percentage carefully.
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