Question
In an election for class president with two contenders,
30% of the cast votes were declared invalid. Of the remaining valid votes, the winner secured 55% and won by a margin of 1,120 votes. How many valid votes were there?Solution
Let the number of votes be '100n' Number of valid votes = 0.7 X 100n = '70n' Number of valid votes received by winning candidate = 0.55 X 70n = '38.5n' Number of valid votes received by losing candidate = 0.45 X 70n = '31.5n' So, 38.5n - 31.5n = 1,120 Or, 7n = 1,120 Or, 'n' = 160 Number of valid votes = 70 X 160 = 11,200
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