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In an election 20% of the voters did not cast their votes and out of the remaining 20% of the votes were found invalid. Two candidates contested the election in which the winning candidate got 64% of the valid votes and won the election by a margin of 3584 votes. Calculate the number of valid votes polled.

In an election 20% of the voters did not cast their votes and out of the remaining 20% of the votes were found invalid. Two candidates contested the election in which the winning candidate got 64% of the valid votes and won the election by a margin of 3584 votes. Calculate the number of valid votes polled. Correct Answer 12800

Given:

20% voters did not cast their votes

20% of the remaining votes were invalid.

Winning candidate got 64% valid votes and won by 3584 votes

Concept:

Total votes is 100%

Total number of votes is sum of votes each candidate gets and invalid votes.

Calculation:

Let the total number of voters be x

Number of votes polled = (100 – 20)% of x

⇒ 80% of x = 4/5x

Number of valid votes = (100 – 20)% of 4/5x

⇒ 80% of 4/5x = 16/25x

Number of votes winning candidate gets = 64% of 16/25x = 0.4096x

Number of votes other candidate gets = (100 – 64)% of 16/25x

⇒ 36% of 16/25x = 0.2304x

⇒ 0.4096x – 0.2304x = 3584

⇒ 0.1792x = 3584

⇒ x = 3584/0.1792

⇒ x = 20000

Valid votes = 16/25 × 20000 = 12800

∴ The valid votes polled is 12800

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