In an election, 80% of eligible voters cast their votes. Of these votes, 5% were declared invalid. If a winning candidate received 11,400 votes, which accounted for 60% of the total valid votes, what was the total number of eligible voters enrolled in that election?

Correct — C. Work backwards from the winner's votes, one percentage at a time.

Valid votes: 60% of valid = 11,400, so valid = 11,400 ÷ 0.60 = 19,000
Votes cast: valid are 95% of cast, so cast = 19,000 ÷ 0.95 = 20,000
Eligible voters: cast are 80% of eligible, so eligible = 20,000 ÷ 0.80 = 25,000 → option (c)

Check forward: 80% of 25,000 = 20,000 cast, 5% invalid leaves 19,000 valid, and 60% of 19,000 = 11,400.

Why the others are wrong

• (a)
  20,000 — 20,000 is the number of votes cast, 80% of the electorate. The question asks for all eligible voters: 20,000 ÷ 0.80 = 25,000.
• (b)
  22,500 — Run it forward: 80% of 22,500 = 18,000 cast, 95% of that = 17,100 valid, and 60% of 17,100 = 10,260, not 11,400.
• (d)
  27,500 — Run it forward: 80% of 27,500 = 22,000 cast, 20,900 valid, and 60% of 20,900 = 12,540, more than the winner's 11,400.

Election questions stack percentages on different bases: turnout is a share of eligible voters, invalid votes a share of votes cast, and the winner's votes a share of valid votes.

Multiply the chain into one factor: 0.80 × 0.95 × 0.60 = 0.456. The winner's 11,400 is 45.6% of the electorate, so the electorate is 11,400 ÷ 0.456 = 25,000.

Key facts

• Valid votes = votes cast × (1 − invalid share): 20,000 × 0.95 = 19,000.
• The winner's 60% is of valid votes, not of all votes cast.
• 0.80 × 0.95 × 0.60 = 0.456, so the winner holds 45.6% of all eligible voters.

Common traps

• Stopping at 20,000, the votes cast, when the question asks for eligible voters.
• Subtracting 5 from 80 to get 75% valid: the 5% is of votes cast, so valid votes are 80% × 95% = 76% of the electorate.

No directly related past PYQ was found.