Question

10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was:

• A. 25000
• B. 33000
• C. 35000
• D. 40000

Hint:

Follow the chain: total voters → voted → valid votes → winner’s majority percentage.

Answer 1

The Correct Option is A

Let the total number of voters be \(N\). Step 1: Voters who cast their vote = \(90%\) of \(N\) = \(0.9N\).
Step 2: Valid votes = \(90%\) of votes cast = \(0.9 \times 0.9N = 0.81N\).
Step 3: Majority fraction = \(54% - 46% = 8%\) of valid votes. \[ \text{Majority} = 0.08 \times 0.81N = 0.0648N \] Step 4: This equals 1620 votes: \[ 0.0648N = 1620 \quad \Rightarrow \quad N = \frac{1620}{0.0648} = 25000 \] \({\text{25000}}\) is correct.