In an election between two candidates, 20% of the 8,000 votes cast were invalid. The winner got 55% of the valid votes. How many valid votes did the loser get?

Think of a college fest election. Some ballots are spoilt (invalid) and are thrown out before counting. Percentages of each candidate are then taken out of the valid pile only. So you work in two layers: first find the valid total from all votes cast, then split the valid total between candidates.

Question: 8,000 votes cast, 20% invalid, winner gets 55% of valid votes. Find the loser's votes.

1. Valid votes = 80% of 8,000 = 6,400.
2. Loser's share = 100% - 55% = 45% of valid votes.
3. Loser = 0.45 x 6,400 = 2,880.
4. Winner = 0.55 x 6,400 = 3,520. Check: 3,520 + 2,880 = 6,400.

A common follow-up: winning margin = 3,520 - 2,880 = 640, which is 10% of valid votes, or 8% of all votes cast.

const valid = 8000 * 0.8;
console.log(Math.round(valid * 0.45)); // Output: 2880
console.log(Math.round(valid * 0.1)); // Output: 640

• Taking 45% of 8,000 instead of the valid 6,400.
• Reporting the margin as a percentage of total votes when the question asks for valid votes, or the other way round.