Question

In an election between two candidates, 12% voters did not cast their vote. \(\frac{1}{6}\)th of the votes casted were found to be invalid. The winner obtained 55% of the valid votes and won the election by 36542 votes. Find the total number of voters registered.

• A. 499500
• B. 498300
• C. 48920
• D. 47580

Hint:

Work backwards from winning margin

Answer 1

The Correct Option is B

Step 1: Define total voters.
Let total registered voters = \(x\). Step 2: Calculate votes cast.
12% did not vote, so votes cast = \(88% \text{ of } x = 0.88x\). Step 3: Calculate valid votes.
Invalid votes = \(\frac{1}{6}\) of votes cast.
Valid votes = \(\frac{5}{6}\) of votes cast = \(\frac{5}{6} \times 0.88x = \frac{4.4}{6}x = \frac{22}{30}x = \frac{11}{15}x\). Step 4: Calculate votes for winner and loser.
Winner gets 55% of valid votes = \(0.55 \times \frac{11}{15}x = \frac{6.05}{15}x\).
Loser gets 45% of valid votes = \(0.45 \times \frac{11}{15}x = \frac{4.95}{15}x\). Step 5: Find winning margin.
Margin = Winner − Loser = \(\frac{6.05 - 4.95}{15}x = \frac{1.1}{15}x = \frac{11}{150}x\).
Given margin = 36542.
\(\frac{11}{150}x = 36542\). Step 6: Solve for \(x\).
\(x = 36542 \times \frac{150}{11}\).
\(36542 \div 11 = 3322\).
\(x = 3322 \times 150 = 498300\).