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Two candidates were standing in an election. Of the total number of people on the electoral roll, 10% did not cast their votes and 600 votes are invalid. The winning candidate secured 60% of the total votes of the voter list and he won the election by 4200 votes. Find how many voters do cast their votes.

Two candidates were standing in an election. Of the total number of people on the electoral roll, 10% did not cast their votes and 600 votes are invalid. The winning candidate secured 60% of the total votes of the voter list and he won the election by 4200 votes. Find how many voters do cast their votes. Correct Answer 10800

Given:

Percentage of people who did not cast their vote = 10%

Number of invalid votes = 600

Percentage of votes secured by winning candidate = 60% of total votes of the voter list

Number of votes by which winning candidate won the election = 4200

Concept used:

Number of voters cast their votes = Total number of voters – Number of voters who cast their votes

Calculation:

Let the total number of voters be x.

Number of voters who casted their votes = x × {(100 – 10)/100}

⇒ x × {90/100}

⇒ 0.90x

Number of valid votes = 0.90x – 600

Number of votes secured by winning candidate = x × (60/100)

⇒ 0.60x

Number of votes secured by losing candidate = 0.60x – 4200

Then, Total number of voters = 0.60x + (0.60x – 4200) + 600 + 0.10x = x

⇒ 1.30x – x = 3600

⇒ 0.30x = 3600

⇒ x = 12000

Number of voters who cast their vote = 12000 × {(100 – 10)/100}

⇒ 12000 × {90/100}

⇒ 10800

∴ The number of voters who cast their votes is 10800.

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