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In an election, 10% of voters do not cast their votes. Out of the total cast votes, 450 becomes invalid. 55% of total valid votes are secured by A and the remaining votes are secured by B. A wins the election by 450 votes. Find the number of voters who did not cast their votes.

In an election, 10% of voters do not cast their votes. Out of the total cast votes, 450 becomes invalid. 55% of total valid votes are secured by A and the remaining votes are secured by B. A wins the election by 450 votes. Find the number of voters who did not cast their votes. Correct Answer 550

Given:

Number of voters who did not cast their votes = 10%

Number of invalid votes = 450

Percentage of votes secured by A = 55% of valid votes

Number of votes by which A wins the election = 450

Concept used:

Number of voters who did not cast their vote = Total number of voters – (Number of votes secured by A + Number of votes secured by B + Invalid votes)

Calculation:

Let the total number of voters be x.

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

⇒ x × {90/100}

⇒ 0.90x

Total number of valid votes = 0.90x – 450

Number of votes secured by A = (0.90x – 450) × (55/100)

⇒ 0.495x – 247.5

Number of votes secured by B = (0.495x – 247.5) - 450

⇒ 0.495x – 697.5

Then, Total number of voters = (0.495x – 247.5) + (0.495x – 697.5) + 450 + 0.1x = x

⇒ 1.09x – x = 495

⇒ 0.09x = 495

⇒ x = 5500

Number of voters who did not cast their vote = 5500 × (10/100)

⇒ 550

∴ The number of voters who did not cast their votes is 550.

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