Question
In an election, candidate 'A' secured 56% of the total
votes cast, while candidate 'B' garnered 85% of the remaining votes. Among the votes received by the candidates, 10% of 'A's votes and 2596 of 'B's votes were declared invalid. The valid votes received by 'A' exceeded those received by 'B' by 60%. Determine the total number of votes cast in the election.Solution
Let the total number of votes cast in the election = '100x' Total number of votes received by 'A' = 100x X 0.56 = '56x' Total number of votes received by 'B' = (100x - 56x) X 0.85 = '37.4x' Number of valid votes received by 'A' = 56x X 0.9 = '50.4x' Number of valid votes received by 'B' = (37.4x - 2596) According to the question, 50.4x ÷ 1.6 = (37.4x - 2596) Or, 31.5x = 37.4x - 2596 So, x = 2596 ÷ 5.9 = 440 So, total number of votes cast in the election = 440 X 100 = 44000
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