In an election between two candidates, the defeated candidate secured 42% of the valid votes polled and lost the election by 2545800 votes. If 365500 votes were declared invalid and 30% people did not cast their vote, what was the approximate number of people (in millions) in the electorate who did NOT cast their votes?

Given:

The defeated candidate secured 42% of the valid votes polled and lost by 2545800 votes.

365500 votes were declared invalid.

30% of people did not cast their vote.

Concept:

To determine the total electorate, we need to calculate the total number of votes and account for the percentage of people who did not vote.

Formula Used:

Total Valid Votes = Votes secured by defeated candidate / Percentage secured by defeated candidate

Total Votes Polled = Total Valid Votes + Invalid Votes

Total Electorate = Total Votes Polled / (1 - Percentage of people who did not vote)

People who did not cast their votes = Total Electorate × Percentage of people who did not vote

Calculation:

⇒ Let the total valid votes be V.

⇒ Defeated candidate secured 42% of valid votes, so:

⇒ V × 42% = 0.42V

⇒ Winning candidate secured (100% - 42%) = 58% of valid votes, so:

⇒ V × 58% = 0.58V

⇒ The difference in votes between the winning and defeated candidate is 2545800:

⇒ 0.58V - 0.42V = 2545800

⇒ 0.16V = 2545800

⇒ V = 2545800 / 0.16

⇒ V = 15911250

⇒ Total Votes Polled = V + Invalid Votes

⇒ Total Votes Polled = 15911250 + 365500

⇒ Total Votes Polled = 16276750

⇒ Total Electorate = Total Votes Polled / (1 - Percentage of people who did not vote)

⇒ Total Electorate = 16276750 / (1 - 0.30)

⇒ Total Electorate = 16276750 / 0.70

⇒ Total Electorate ≈ 23252500

⇒ People who did not cast their votes = Total Electorate × Percentage of people who did not vote

⇒ People who did not cast their votes = 23252500 × 0.30

⇒ People who did not cast their votes ≈ 6975750

∴ The approximate number of people (in millions) in the electorate who did NOT cast their votes is 7 million.