Question
Download Solution PDFIn an election between two candidates, 15% of the voters in the voters' list did not cast their votes and 10% of the votes polled were declared invalid. The winning candidate got 60% of the total valid votes and won by a majority of 7650 votes. The number of valid votes was :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Percentage of voters who did not cast their votes = 15%
Percentage of votes polled declared invalid = 10%
The winning candidate got 60% of the total valid votes.
Majority = 7650 votes
Calculation:
Let V be the total number of voters in the voters' list.
Voters who did not cast votes = 15% of V = 0.15V
Votes polled (casted votes) = V - 0.15V = 0.85V
Valid votes = 90% of Votes polled = 0.90 × (0.85V) = 0.765V
Votes for the winning candidate = The winning candidate got 60% of the total valid votes.
Winning candidate's votes = 0.60 × (Valid votes)
Votes for the losing candidate = 40% of the total valid votes.
Losing candidate's votes = 0.40 × (Valid votes)
Winning candidate's votes - Losing candidate's votes = 7650
0.60 × (Valid votes) - 0.40 × (Valid votes) = 7650
0.20 × (Valid votes) = 7650
Valid votes = 7650 / 0.20
Valid votes = 7650 × (100 / 20)
Valid votes = 7650 × 5
Valid votes = 38250
∴ The correct answer is option 2.
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