In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

Question: In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

Solution:
Invalid votes = 15% of 8000 = (15/100) × 8000 = 1200

∴ Valid votes = 8000 - 1200 = 6800
Now,
Votes for A and B = 30% + 45% = 75% of 6800 = (75/100) × 6800 = 5100

∴ Votes for C = 6800 - 5100 = 1700

∴ So Candidate C received 1700 valid votes.