Question
In a Lok Sabha election, two candidates vied for a
parliamentary seat. Out of the total eligible voters in the constituency, 20% opted not to exercise their right to vote. Among the cast votes, 25% were deemed invalid. The winning candidate secured three times the number of votes garnered by the losing candidate, with a vote margin of 3,000. Calculate the total number of eligible voters in the constituency.Solution
ATQ, Let the total number of voters in the constituency = '100p' Number of votes cast = (100 - 20)% of 100p = 80% of 100p = '80p' Number of valid votes = (100 - 25)% of 80p = 75% of 80p = '60p' Let the number of votes received by losing candidate = 'q' So, the number of votes received by winning candidate = 3 × q = '3q' So, 3q - q = 3,000 Or, 2q = 3,000 Or, q = 1,500 Also, 3q + q = 60p Or, 60p = 4q = 4 × 1500 Or, 60p = 6,000 Or, p = 100 Total number of voters in the constituency = 100p = 100 × 100 = 10,000
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