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In an election between two candidates, one candidate got 40% of total votes and yet lost by 1000 votes. If all the votes polled were valid, then the total number of votes cast in the election was:
6000
5000
10000
8000
5000
Calculate the percentage gap (60% - 40% = 20%). Since 20% of the total votes equals 1000, the total (100%) is 1000 / 0.20 = 5000.
One candidate received 40% of votes, the other candidate received 60% of votes. The losing candidate lost by 1000 votes.
VtotalтАЛ=Percentage┬аdifferenceDifference┬аin┬аvotesтАЛ
Calculate the percentage gap (60% - 40% = 20%). Since 20% of the total votes equals 1000, the total (100%) is 1000 / 0.20 = 5000.
Many students subtract 40% from 100% and calculate 60% of 1000 instead of identifying the vote difference percentage gap between candidates.
Calculate Percentage Share
If one candidate got 40% of the votes, the other candidate (the winner) received 100% - 40% = 60%.
60%тИТ40%=20%┬а(vote┬аgap)
Establish the Relationship
The problem states the loser lost by 1000 votes. This represents the 20% difference in total votes.
20%┬аof┬аVtotalтАЛ=1000
Calculate Total Votes
Solving for the total number of votes VtotalтАЛ:
VtotalтАЛ=0.201000тАЛ=5000
B is correct because the percentage difference of 20% between candidates equals 1000 votes, leading to a total of 5000 votes.
This concept of a 'percentage gap' is fundamental in profit/loss problems and election-based reasoning questions across competitive exams.
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