In an election, 2 candidates participated. 10% of votes were declared

1.	In an election, 2 candidates participated. 10% of votes were declared invalid and the winner got 60% of the valid votes and won by 900 votes. Find the total number of voters.1. 55002. 45003. 50004. 56005. None of these
Answer» Correct Answer - Option 3 : 5000 Given: Percentage of invalid votes = 10% Percentage of valid votes winner got = 60% Extra votes that the winning candidate got than losing candidate = 900 Concept used: Total number of voters = Invalid votes + Number of votes secured by A + Number of votes secured by B Calculation: Let the total number of voters be x. Number of valid votes = x × {(100 – 10)/100} ⇒ x × {90/100} ⇒ 0.90x Number of votes that the winning candidates got = 0.90x × (60/100) ⇒ 0.54x Number of votes that the losing candidates got = 0.54x – 900 Then, Total number of votes = 0.10x + 0.54x + 0.54x – 900 = x ⇒ 1.18x – 900 = x ⇒ 0.18x = 900 ⇒ x = 5000 ∴ The total number of voters is 5000.

In an election, 2 candidates participated. 10% of votes were declared invalid and the winner got 60% of the valid votes and won by 900 votes. Find the total number of voters.1. 55002. 45003. 50004. 56005. None of these

Answer» Correct Answer - Option 3 : 5000

Given:

Percentage of invalid votes = 10%

Percentage of valid votes winner got = 60%

Extra votes that the winning candidate got than losing candidate = 900

Concept used:

Total number of voters = Invalid votes + Number of votes secured by A + Number of votes secured by B

Calculation:

Let the total number of voters be x.

Number of valid votes = x × {(100 – 10)/100}

⇒ x × {90/100}

⇒ 0.90x

Number of votes that the winning candidates got = 0.90x × (60/100)

⇒ 0.54x

Number of votes that the losing candidates got = 0.54x – 900

Then, Total number of votes = 0.10x + 0.54x + 0.54x – 900 = x

⇒ 1.18x – 900 = x

⇒ 0.18x = 900

⇒ x = 5000

∴ The total number of voters is 5000.