In an election, there were four candidates, and 80% of the registered voters cast their votes. One of the candidates received 30% of the cast votes, while the other three candidates received the remaining cast votes in the proportion 1:2:3. 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:

Question

Accepted Answer

* One candidate received **30% of the polled votes**.
* The remaining **70%** was shared among three other candidates in the ratio **1 : 2 : 3**.
* Hence, the overall vote distribution ratio becomes:

$$
  30\% : 70\%(1 : 2 : 3) = 3 : 7(1 : 2 : 3)
  $$

Multiply to get:

$$
  3 : 7 : 14 : 21
  $$

Now, multiply each term by 6 to avoid fractions:

$$
  18 : 7 : 14 : 21
  $$

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### Let actual votes be:

* Candidate A = 18x
* Candidate B = 7x
* Candidate C = 14x
* Candidate D = 21x

It is given that the **winner received 2512 votes more** than the candidate with the **second-highest votes**.

* Winner: 21x
* Second-highest: 18x

$$
21x - 18x = 3x = 2512 \Rightarrow x = \frac{2512}{3}
$$

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### Total Polled Votes:

$$
= 18x + 7x + 14x + 21x = 60x = 60 	imes \frac{2512}{3} = 20 	imes 2512 = 50,240
$$

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### Registered Voters:

Given that **polled votes = 80% of total registered votes**, we get:

$$
	ext{Total registered votes} = \frac{50,240}{0.8} = 62,800
$$

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### Final Answer:

**62,800**
**Choice D** is correct.

Answer

Answer

Answer