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In an election, two candidates participated in which 20% of voters of the voting list did not vote, 3500 votes declared invalid and the winner gets 60% votes of the valid votes and wins by 5000 votes. Find the number of voters who appeared for voting?
1. 27500
2. 29500
3. 30000
4. 28500

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Correct Answer - Option 4 : 28500

Given:

20% of voters did not vote.

3500 votes were declared invalid.

The winner gets 60% of valid votes and wins by 5000 votes.

Formula used:

Percentage = (Value ⁄ Total Value) × 100

Calculation:

Let the total vote be ‘x’.

20% did not vote on the total voting list.

Number of voters appeared for voting = x × 80/100

⇒ Invalid votes = 3500

⇒ Valid votes = x × 80/100 – 3500

Difference between wining and losing candidate = 60 – 40 = 20% of valid votes

⇒ (x × 80/100 – 3500) × 20/100 = 5000

⇒ 4x/5 – 3500 = 25000

⇒ 4x/5 = 25000 + 3500

⇒ x = (28500 × 5)/4

⇒ x = 35625

Number of voters appeared for voting = x × 80/100

⇒ Number of voters appeared for voting = 35625 × 80/100

⇒ 28500

∴ Number of voters appeared for voting = 28500

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