Percentages · Topic 5 of 6

🗳️ Election & Voting

1 exam question type, fully solved

The whole game is keeping straight which base each percent sits on: the full voter list, the votes actually polled, or the valid votes.

Margin shortcut + peel the layers

The winning margin is NOT the winner's share. In a two-way race where the winner gets p%, the loser gets (100−p)%, so the margin = (2p − 100)% of the valid votes. A 65%–35% split is a 30% margin.

When invalid votes or no-shows appear, peel down in order:

list → votes polled (remove no-shows) → valid votes (remove invalid) → margin.

The winner's % and the margin both sit on the valid votes, never on the full list.

🗳️Election FunnelPeel base by base

voters on list

% didn't vote

% of polled invalid

winner % of valid

1 · voter list

10,000

2 · votes polled (−20% no-shows)

8,000

3 · valid votes (−5% invalid)

7,600

4 · winner 60% 🟩 vs loser 40% 🟥 of VALID

4,560 / 3,040

Peel the bases top to bottom — each % sits on the layer above it: List 10,000 → polled = 10,000 × 0.8 = 8,000 Polled 8,000 → valid = 8,000 × 0.95 = 7,600 Winner = 60% of 7,600 = 4,560 · loser = 7,600 − 4,560 = 3,040

Margin = 4,560 − 3,040 = 1,520 votes

Margin rule: (2p − 100)% = (2×60 − 100)% = 20% of 7,600 valid votes = 1,520 ✓

Winner gets 60% in a two-way race; the margin is (2×60 − 100) = % of the votes.

Q1A winner gets 60% of votes in a two-way race and wins by 2,000. Total votes:

Q2A candidate got 48% of valid votes and lost by 480. Total valid votes:

Q3A candidate got 5,400 votes = 45% of valid votes. Valid votes:

📚

Real exam questions — Election & Voting

1 question types · 4 solved examples from real SSC papers

The whole game is which base each percent sits on: the full list, the votes polled, or the valid votes.

How to solve this type

The winner's margin is the percentage difference of the total valid votes, not the winner's own share. In a two-candidate contest where the winner gets

p\%

, the loser gets

(100-p)\%

, so the margin is

(2p-100)\%

of the valid votes. When invalid votes or no-shows are mentioned, first peel down to the valid pool: list → votes polled (remove no-shows) → valid (remove invalid), then apply the candidate percentages to that valid pool. Convert awkward percentages to fractions and divide early (e.g. divide a

55\%

value by 11 to reach

5\%

) to keep the arithmetic light. Never equate the winner's percentage directly to the margin — that is the classic trap.

In a two-candidate election the winner gets $65\%$ of the votes and wins by a margin of 3000 votes. The total number of votes is:

A10,000B8,000C15,000D12,000

A candidate secured 42,680 votes, which was $55\%$ of the total valid votes. The total number of valid votes was:

A77,000B76,000C77,600D78,000

In an election $75\%$ of the enrolled voters cast their votes and $4\%$ of those were invalid. The winner got $60\%$ of the valid votes and won by 14,400 votes. The number of enrolled voters is:

A80,000B90,000C1,20,000D1,00,000

Out of 7,50,000 enrolled voters, a candidate received 3,82,500 votes, which was $60\%$ of the total valid votes. The percentage of invalid votes is:

A15%B18%C20%D12%