In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A…

Question

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 were 75% of the total valid votes. Find the total number of voters enrolled in that election.

1. A. 17,500
2. B. 16,800 (Correct answer)
3. C. 18,000
4. D. 15,500

Correct Answer

Option B — 16,800

Detailed Solution & Explanation

The correct answer is 16,800.

Key Points

• The candidate's 9261 votes are 75% of the valid votes, so valid votes = 9261 ÷ 0.75 = 12348.
• Valid votes are 98% of those cast (2% invalid), so votes cast = 12348 ÷ 0.98 = 12600.
• Votes cast are 75% of enrolled voters, so enrolled = 12600 ÷ 0.75 = 16800.

Note

• Work backwards through each percentage in turn; trying to combine them in one step is where most errors creep in.

Additional Information

• Nested-percentage questions like this are solved by unwinding the chain backwards, dividing at each stage rather than multiplying:
  • votes won → valid votes (÷ 0.75)
  • valid votes → votes cast (÷ 0.98)
  • votes cast → total voters (÷ 0.75)
• Setting it out as a chain first prevents the common error of applying the percentages to the wrong base — the 2% invalid applies to votes cast, not to the electorate.
• A quick check on the final figure: 75% of 16,800 is 12,600 cast, of which 98% is 12,348 valid, and 75% of that is 9,261.