In an election between two candidates, 75% of the voters cast their votes, out…
2022
In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which is 75% of the total valid votes. Find the total number of voters enrolled in that election.
Answer: D. 16800 — When a quantity passes through several percentage-based stages in sequence, the value at the end of the chain equals the original amount multiplied by the…
- A.
16000
- B.
15800
- C.
15080
- D.
16800
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Correct answer: D
When a quantity passes through several percentage-based stages in sequence, the value at the end of the chain equals the original amount multiplied by the product of every stage's fraction. To recover the original amount from a value further down the chain, divide by that same product — this is the reverse-percentage / successive-percentage technique.
Let the total number of voters enrolled be V.
75% of the voters cast their votes, so the votes cast = 0.75V.
2% of the votes cast were invalid, so 98% were valid: valid votes = 0.98 x 0.75V = 0.735V.
The candidate received 75% of the valid votes: candidate's votes = 0.75 x 0.735V = 0.55125V.
This equals the given figure: 0.55125V = 9261, so V = 9261 / 0.55125 = 16800.
Substituting V = 16800 back in: votes cast = 0.75 x 16800 = 12600; valid votes = 0.98 x 12600 = 12348; the candidate's votes = 0.75 x 12348 = 9261, matching the given figure and confirming the total enrolled voters.