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In an election; There are two candidates. If 10% of the voters did not vote and 10% votes were declared invalid and the winner gets 75% of the valid votes and wins by 4050 votes. What is the total number of voters on the voting list?

In an election; There are two candidates. If 10% of the voters did not vote and 10% votes were declared invalid and the winner gets 75% of the valid votes and wins by 4050 votes. What is the total number of voters on the voting list? Correct Answer 10,000

Given: 

10% of voters did not vote.

Total invalid votes = 10%

The winner got 75% of the votes and won by 4050 votes.

Calculation:

Let the total voters be 100x.

Votes cast = 90% of 100x = 90x      

Invalid votes = 10% of 90x = 9x

Total valid votes = 90x - 9x = 81x

Total number of valid votes got by the winning candidate = 75% of 81x 

Total number of valid votes got by losing candidate = 25% of 81x

According to the question,

Difference in votes = 4050

The votes got by winning candidate - Votes got by losing candidate = 4050

⇒ 75% of 81x - 25% of 81x = 4050

⇒ 50% of 81x = 4050

⇒ (1/2) of 81x = 4050

⇒ (1/2) of 81x = 4050

⇒ x = 100

Total votes = 100x = 10,000

∴ Total number of voters on the voting list is 10,000 

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