Discussion
In a college election between two candidates, one candidate got 45% of the total valid votes. 20% of the votes were invalid. If the total votes were 14,500, then what is the number of valid votes which the other candidate got ?
Answer: A
The other candidate got 6,380 valid votes.
20% of the votes were invalid, so 80% were valid. The first candidate got 45% of the valid votes, so the other got 55%:
\[ \begin{aligned} \text{valid} &= 0.8 \times 14500 = 11600 \\ \text{other} &= 0.55 \times 11600 = 6380 \end{aligned} \]
5,220 is the first candidate's share, and 6,525 and 7,975 come from taking 45% or 55% of all 14,500 votes instead of the valid ones.
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