Question
At an election between three candidates P. Q and R, 20%
of the votes polled were declared invalid. Out of the valid votes P gets 30% votes. The remaining valid votes were shared by Q and R in the ratio 11: 9, respectively. If P has received 150 votes less than R, then find the total number of votes polled.Solution
Let the total number of votes polled be x. Number of valid votes = 80% of x Number of votes secured by P = 30% of 80% of x Remaining valid votes = 70% of 80% of x Number of votes secured by R = (9/20) of 70% of 80% of x Votes received by P = Votes received by R - 150 => 30% of 80% of x = (9/20) of 70% of 80% of x - 150 => 150 = (9/20) of 56% of x - 24% of x => x = 12500 ∴ The total votes polled was 12500.
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