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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 : 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
  • a)
    50240
  • b)
    62800
  • c)
    60288
  • d)
    40192
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In an election, there were four candidates and 80% of the registered v...
Let's break down the problem step by step:

Step 1: Calculate the number of casted votes
We know that 80% of the registered voters casted their votes. Let's assume the number of registered voters as 'x'. Therefore, the number of casted votes would be 80% of 'x', which is 0.8x.

Step 2: Calculate the number of casted votes for the first candidate
We are given that one of the candidates received 30% of the casted votes. Therefore, the number of votes received by the first candidate would be 30% of 0.8x, which is 0.24x.

Step 3: Calculate the proportion of votes received by the other three candidates
We are given that the remaining three candidates received votes in the proportion 1:2:3. Let's assume the number of votes received by the second candidate as 'y'. Therefore, the number of votes received by the third and fourth candidates would be 2y and 3y, respectively.

Step 4: Calculate the total number of votes received by all candidates
The total number of votes received by all candidates would be the sum of the votes received by each candidate. Therefore, the equation becomes:
0.24x + y + 2y + 3y = 0.24x + 6y = 0.8x

Step 5: Find the value of y
To find the value of 'y', we need to solve the equation 0.24x + 6y = 0.8x. Simplifying the equation, we get:
6y = 0.56x
y = 0.56x/6
y = 0.0933x

Step 6: Calculate the difference in votes between the winner and the candidate with the second highest votes
We are given that the winner of the election received 2512 votes more than the candidate with the second highest votes. Therefore, the equation becomes:
0.24x - y = 2512
0.24x - 0.0933x = 2512
0.1467x = 2512
x = 2512/0.1467
x ≈ 17117.6

Step 7: Calculate the number of registered voters
Finally, to find the number of registered voters, we need to round up the value of 'x' to the nearest whole number, as we can't have a fraction of a voter. Therefore, the number of registered voters is approximately 17118.

The correct answer is option B) 62800.
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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 : 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 wasa)50240b)62800c)60288d)40192Correct answer is option 'B'. Can you explain this answer?
Question Description
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