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In this election, there are only two candidates. 25 percent of the voters in the election did not cast their votes. The winner got 64% of the remaining votes. Then find the ratio between the number of voters in the election who did not cast their votes and the votes obtained by the loser.

In this election, there are only two candidates. 25 percent of the voters in the election did not cast their votes. The winner got 64% of the remaining votes. Then find the ratio between the number of voters in the election who did not cast their votes and the votes obtained by the loser. Correct Answer None of these

Given:

25% of the voters in this election did not cast their votes.

The winner got 64% of the remaining votes.

Formula used:

Percentage formula = (Value / Total value) × 100

Total voters = cast votes + votes that did not casted

Calculation:

Let total votes in election = 100%

The number of voters who did not cast their votes = 25%

Remaining votes = 100 – 25 = 75%

Now the winner got 64% of the remaining votes.

So the loser got 36% votes of the remaining votes

⇒ (36 / 100) × 75 = 27%

∴ The ratio between the number of voters in the election who did not cast their votes and the votes obtained by the loser is = 25% ∶ 27% = 25 ∶ 27.

Detailed Solution:

Let the total number of votes be x.

25% of the voters in this election did not cast their votes.

Now, the number of voters who did not cast their votes = (25 / 100) × x = x / 4 votes

Remaining votes

⇒ x – (x / 4) = 3x / 4 votes

By question, the winner got 64% of the remaining votes

Now, the number of votes that obtained by the winner = (64 / 100) × (3x / 4) = 12x / 25 votes

Then the number of votes that obtained by looser

⇒ remaining votes – the number of votes that obtained by the winner

⇒ (3x / 4) – (12x / 25) = (75x – 48x) / 100 = 27x / 100 votes

Now to find the ratio between voters who did not cast their votes and the number of votes that obtained by looser

⇒ (x / 4) ∶ (27x / 100) = 25 ∶ 27

∴ The ratio between the number of voters in the election who did not cast their votes and the votes obtained by the looser is 25 ∶ 27.

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