In an election, 80% of eligible voters cast their votes. Of these votes, 5% were declared invalid. If a winning candidate receive…

Question

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?

1. A. 20000
2. B. 22500
3. C. 25000 (Correct answer)
4. D. 27500

Correct Answer

Option C — 25000

Detailed Solution & Explanation

The correct answer is 25000.

Key Points

• Work backwards from the winner's votes:
  • 11,400 is 60% of the valid votes → valid votes = 11,400 ÷ 0.60 = 19,000
  • Valid votes are 95% of the votes cast (5% invalid) → votes cast = 19,000 ÷ 0.95 = 20,000
  • Votes cast are 80% of eligible voters → eligible = 20,000 ÷ 0.80 = 25,000

Additional Information

• Each percentage applies to a different base — valid votes to votes cast, votes cast to eligible voters — and mixing the bases is the error the question is built around.
• Multiplying forward confirms the chain: 25,000 × 0.8 = 20,000; × 0.95 = 19,000; × 0.6 = 11,400 ✓.
• The combined factor is 0.8 × 0.95 × 0.6 = 0.456, so the winner's votes are 45.6% of all eligible voters — a useful single-step check.

प्रश्न (हिन्दी में)

एक चुनाव में, 80% योग्य मतदाताओं ने अपने वोट डाले। इनमें से 5% वोट अवैध घोषित कर दिए गए। यदि एक विजयी उम्मीदवार को 11,400 वोट मिले, जो कुल वैध वोटों का 60% है, तो उस चुनाव में नामांकित कुल योग्य मतदाताओं की संख्या कितनी थी?

1. A. 20000
2. B. 22500
3. C. 25000
4. D. 27500