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In an election, every voter has to cast his vote for two candidates. Half of the total voters give one vote to A and other vote to B, C and D in the ratio 3 : 2 : 1. The half of the rest votes give one vote to B and other vote to C and D in the ratio 2 : 1. The half of the remaining voters give equal votes to C and D. Other 840 voters did not cast their votes. Find the number of votes received by C. 
  • a)
    2000
  • b)
    6005 
  • c)
    3080 
  • d)
    3000 
Correct answer is option 'C'. Can you explain this answer?
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In an election, every voter has to cast his vote for two candidates. H...
Let total voter=200 (every voter cost two vote
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In an election, every voter has to cast his vote for two candidates. H...
Given:
- In an election, every voter has to cast his vote for two candidates.
- Half of the total voters give one vote to A and other vote to B, C and D in the ratio 3 : 2 : 1.
- The half of the remaining votes give one vote to B and other vote to C and D in the ratio 2 : 1.
- The half of the remaining voters give equal votes to C and D.
- 840 voters did not cast their votes.

To find:
The number of votes received by candidate C.

Solution:
Let's assume the total number of voters as 'x'.

Step 1: Votes for A, B, C, D
- Half of the total voters give one vote to A and other vote to B, C, and D in the ratio 3 : 2 : 1.
- So, the number of votes for A = x/2 and the number of votes for B, C, and D = (x/2) * (3+2+1) = (x/2) * 6 = 3x.

Step 2: Remaining Votes
- The remaining votes are (x - x/2) = x/2.
- Half of these votes give one vote to B and the other vote to C and D in the ratio 2 : 1.
- So, the number of votes for B = (x/2)/2 * 2 = x/2 and the number of votes for C and D = (x/2)/2 * 1 = x/4.

Step 3: Final Votes
- The remaining voters are (x/2 - x/4) = x/4.
- Half of these voters give equal votes to C and D.
- So, the number of votes for C and D = (x/4)/2 * 1 = x/8.

Step 4: Total Votes
- Adding up the votes for A, B, C, and D:
- Votes for A = x/2
- Votes for B = 3x
- Votes for C = x/4
- Votes for D = x/8
- Total votes = (x/2) + 3x + (x/4) + (x/8) = 4x + 4x + x + x/2 = 9.5x.

Step 5: Equating Total Votes
- Total votes = 9.5x
- 840 voters did not cast their votes.
- So, the total votes should be equal to the total number of voters minus 840.
- 9.5x = x - 840.

Step 6: Solving the equation
- Subtracting 'x' from both sides: 8.5x = -840.
- Dividing both sides by 8.5: x = -840/8.5.
- x = -98.82352941176471.

Step 7: Conclusion
- The number of votes cannot be negative, so there is an error in the given information or question.
- The given information is inconsistent or incorrect.
- Therefore, it is
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In an election, every voter has to cast his vote for two candidates. Half of the total voters give one vote to A and other vote to B, C and D in the ratio 3 : 2 : 1. The half of the rest votes give one vote to B and other vote to C and D in the ratio 2 : 1. The half of the remaining voters give equal votes to C and D. Other 840 voters did not cast their votes. Find the number of votes received by C.a)2000b)6005c)3080d)3000Correct answer is option 'C'. Can you explain this answer?
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