Single correct option
In an election between two candidates, 10% of the voters on the list did not vote and 60 of the votes cast were declared invalid. The winning candidate received votes equal to 47% of the voters on the list and won by 1660 votes. The number of voters on the list was
- A. 45,500
- B. 40,000
- C. 42,000
- D. 38,500
Show answer and solution
Answer: (B) 40,000
Let the list have N voters. 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 = 1660 → 0.04N = 1600 → N = 40,000.
The common error is to forget the 60 invalid votes, which gives 0.04N = 1660 and N = 41,500 (not an option, but a trap in similar questions).
Winner = 0.47N; loser = (0.9N − 60) − 0.47N = 0.43N − 60.
Margin = 0.47N − (0.43N − 60) = 0.04N + 60 = 1660 → 0.04N = 1600 → N = 40,000.
The common error is to forget the 60 invalid votes, which gives 0.04N = 1660 and N = 41,500 (not an option, but a trap in similar questions).
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