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In an election between two candidates, 80% of the voters cast their votes. 5% of the votes cast were declared invalid. A candidate got 7600 votes which were 50% of the total valid votes. The total number of voters enrolled in that election was:
20000
25000
18000
22000
20000
Work backward: 7600├Ч2=15200 (total valid), then 15200├╖0.95=16000 (total cast), then 16000├╖0.8=20000.
Voters who cast their votes = 80%, invalid votes = 5% of votes cast, candidate votes = 7600 (which is 50% of valid votes).
Total┬аVoters=Percentage┬аof┬аValid┬аVotesCandidate┬аVotesтАЛ├ЧValid┬аPercentage100тАЛ├ЧVoting┬аPercentage100тАЛ
Work backward: 7600├Ч2=15200 (total valid), then 15200├╖0.95=16000 (total cast), then 16000├╖0.8=20000.
Students often subtract 5% from 80% (i.e., 75%) instead of calculating 5% of the 80% or correctly applying the reduction on the subset.
Calculate total valid votes
Since 7600 votes represent 50% of total valid votes, the total valid votes are 7600├Ч2=15200.
15200=0.507600тАЛ
Calculate total votes cast
Since 5% of cast votes were invalid, 95% were valid. Thus, total cast votes = 15200/0.95=16000.
16000=0.9515200тАЛ
Calculate total enrolled voters
Since 80% of total enrolled voters cast their votes, total voters = 16000/0.80=20000.
20000=0.8016000тАЛ
A is correct because the step-by-step reverse calculation of the voting percentages yields a total of 20000 voters.
This concept of sequential percentage reduction is identical to calculating successive discounts in profit and loss problems.
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