In an election two candidates participated, the winner got 60% of the total valid votes, 30% of the votes were declared as invalid. If the total number of votes was 8000, the number of valid votes that the other candidate got was.
Election Vote Calculation Explained
This problem involves calculating the number of valid votes received by the losing candidate in an election. We are given the total number of votes, the percentage of invalid votes, and the percentage of valid votes the winner received.
Understanding the Election Data
Let's break down the information provided:
- Total Votes Cast: 8000
- Percentage of Invalid Votes: 30%
- Winner's Share: 60% of the total valid votes
Step-by-Step Calculation
1. Calculate the Number of Invalid Votes
The invalid votes are 30% of the total votes.
Number of Invalid Votes = $30\% \times \text{Total Votes}$
Number of Invalid Votes = $\frac{30}{100} \times 8000$
Number of Invalid Votes = $0.30 \times 8000 = 2400$ votes.
2. Calculate the Total Number of Valid Votes
The total valid votes are the total votes minus the invalid votes.
Total Valid Votes = Total Votes - Number of Invalid Votes
Total Valid Votes = $8000 - 2400 = 5600$ votes.
3. Calculate the Winner's Valid Votes
The winner received 60% of the total valid votes.
Winner's Votes = $60\% \times \text{Total Valid Votes}$
Winner's Votes = $\frac{60}{100} \times 5600$
Winner's Votes = $0.60 \times 5600 = 3360$ votes.
4. Calculate the Other Candidate's Valid Votes
The other candidate (the loser) received the remaining valid votes.
Other Candidate's Votes = Total Valid Votes - Winner's Votes
Other Candidate's Votes = $5600 - 3360 = 2240$ votes.
Alternatively, the other candidate received (100% - 60%) = 40% of the total valid votes.
Other Candidate's Votes = $40\% \times \text{Total Valid Votes}$
Other Candidate's Votes = $\frac{40}{100} \times 5600 = 0.40 \times 5600 = 2240$ votes.
Summary Table
| Total Votes | 8000 |
| Invalid Votes (30%) | 2400 |
| Total Valid Votes | 5600 |
| Winner's Votes (60% of Valid) | 3360 |
| Other Candidate's Votes (40% of Valid) | 2240 |
Conclusion
The number of valid votes that the other candidate got was 2240.
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