Single correct option
In an election between two candidates, 10% of the voters on the voter list did not vote and 60 of the 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 1,308 votes. How many voters were on the list?
- A. 31,200
- B. 28,800
- C. 32,700
- D. 30,600
Show answer and solution
Answer: (A) 31,200
Let the list have N voters. 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 = 1308 ⇒ 0.04N = 1248 ⇒ N = 31,200.
Check: cast = 28,080; valid = 28,020; winner = 14,664; loser = 13,356; difference = 1,308 ✓.
The trap is to forget the 60 invalid votes, which gives N = 32,700.
Winner = 0.47N, so loser = 0.9N − 60 − 0.47N = 0.43N − 60.
Margin: 0.47N − (0.43N − 60) = 0.04N + 60 = 1308 ⇒ 0.04N = 1248 ⇒ N = 31,200.
Check: cast = 28,080; valid = 28,020; winner = 14,664; loser = 13,356; difference = 1,308 ✓.
The trap is to forget the 60 invalid votes, which gives N = 32,700.
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