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In an election between two candidates, one got 55% of the total valid votes, and 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got was:
2600
2700
3000
3300
2700
Calculate valid votes as 80% of 7500 (6000). The other candidate gets 45% (100% - 55%) of 6000. 0.45├Ч6000=2700.
Total votes = 7500. Invalid votes = 20%. One candidate received 55% of valid votes.
V=T├Ч(1тИТi)├Ч(1тИТv)
Calculate valid votes as 80% of 7500 (6000). The other candidate gets 45% (100% - 55%) of 6000. 0.45├Ч6000=2700.
Students often calculate the other candidate's votes as 45% of the total 7500 votes, forgetting to subtract the invalid votes first.
Calculate Invalid Votes
Find the total number of invalid votes by taking 20% of the total 7500.
7500├Ч0.20=1500
Calculate Total Valid Votes
Subtract the invalid votes from the total votes.
7500тИТ1500=6000
Calculate Other Candidate's Percentage
Since one candidate received 55% of valid votes, the other candidate received 100% - 55% = 45%.
100%тИТ55%=45%
Final Calculation
Find 45% of the total valid votes (6000).
6000├Ч0.45=2700
B is correct because the number of valid votes for the other candidate is 45% of the 6000 valid votes, which equals 2700.
This logic is identical to 'Profit and Loss' where you calculate the selling price after a discount or tax reduction, applying percentages sequentially.
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