Question

In an election,there were four candidates and $80\%$ of the registered voters casted their votes.One of the candidates received $30\%$ of the casted votes while the other three candidates received the remaining casted votes in the proportion $1\ratio2\ratio3$.If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

• A. 40192
• B. 60288
• C. 50240
• D. 62800

Answer 1

Answer: (D)

62800

Answer 2

The correct answer is D: 62800
Let the number of registered voters be (100x).
Number of votes casted=(80x)
Votes received by one of the candidates=$(\frac{30}{100} \times 80x = 24x)$
Remaining votes=(80x-24x=56x)
Votes received by the other three candidates are:$(6 \times \frac{56x}{6}, 2 \times \frac{56x}{6}, 3 \times \frac{56x}{6})$
So,their votes are (28x,112x,168x) respectively.
Given that (28x-24x=2512)
Solving for (x), we get (x=628).
Therefore,the number of registered voters=$(100x=100 \times 628 = 62800)$.
Hence,the answer is (62800),which matches the given answer.