In an election between two candidates, 10% of the voters did not cast their votes and 5% of the votes polled were found invalid. The successful candidate got 52.5% of the valid votes and won by a majority of 1710 votes. The number of voters enrolled on the voters list was:

Given:

10% of the voters did not cast their votes and 5% of the votes polled were found invalid. The successful candidate got 52.5% of the valid votes and won by a majority of 1710 votes.

Concept Used:

Calculate the total number of voters enrolled based on the given percentages and majority votes.

Calculation:

Let the total number of voters enrolled be x .

10% of the voters did not vote:

⇒ Voters who did not vote = 0.10x

⇒ Voters who voted = x - 0.10x = 0.90x

5% of the votes polled were invalid:

⇒ Invalid votes = 0.05 × 0.90x = 0.045x

⇒ Valid votes = 0.90x - 0.045x = 0.855x

The successful candidate got 52.5% of the valid votes:

⇒ Votes received by successful candidate = 0.525 × 0.855x = 0.448875x

Let the votes received by the other candidate be y .

⇒ Total valid votes = Votes received by successful candidate + Votes received by the other candidate

⇒ 0.855x = 0.448875x + y

⇒ y = 0.855x - 0.448875x = 0.406125x

The majority is 1710 votes:

⇒ 0.448875x - 0.406125x = 1710

⇒ 0.04275x = 1710

⇒ x = \(\frac{1710}{0.04275}\)

⇒ x = 40000

∴ The number of voters enrolled on the voters list was 40000.