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      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?
      A 13,000 Correct Answer Incorrect Answer
      B 16,400 Correct Answer Incorrect Answer
      C 12,150 Correct Answer Incorrect Answer
      D 11,200 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      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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