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?

The correct option is 7.

Let the total number of people in the electorate be $E$.

According to the problem statement:
1. 30% of the electorate did not cast their vote.
2. The remaining 70% of the electorate cast their votes.
3. Among the cast votes, 365,500 votes were declared invalid.
4. In the valid votes, the defeated candidate secured 42% of the valid votes.
5. The defeated candidate lost by 2,545,800 votes.

Let the total number of valid votes be $V$.

Since the defeated candidate received 42% of the valid votes, the winning candidate must have received the remaining percentage of valid votes:
Percentage of valid votes secured by winner = 100% - 42% = 58%

The difference in percentage of votes between the winner and the loser is:
58% - 42% = 16% of the valid votes ($V$)

We are given that this margin of defeat is equal to 2,545,800 votes.
Therefore:

$16\%\text{ of }V=\mathrm{2,545,800}$

$\frac{16}{100}\times V=\mathrm{2,545,800}$

$V=\frac{\mathrm{2,545,800}\times 100}{16}$

$V=\mathrm{15,911,250}$

So, the total number of valid votes polled is 15,911,250.

Next, we find the total number of votes cast. The total votes cast equals the sum of valid votes and invalid votes:
Total votes cast = $V+\mathrm{365,500}$

$\text{Total votes cast}=\mathrm{15,911,250}+\mathrm{365,500}=\mathrm{16,276,750}$

We know that 30% of the electorate did not cast their vote, which means 70% of the electorate cast their votes.
Let $E$ be the total electorate. Then:

$70\%\text{ of }E=\mathrm{16,276,750}$

$\frac{70}{100}\times E=\mathrm{16,276,750}$

$E=\frac{\mathrm{16,276,750}\times 100}{70}=\mathrm{23,252,500}$

Now, we need to find the number of people who did NOT cast their votes (30% of the electorate $E$):

$\text{People who did not vote}=30\%\text{ of }E$

$\text{People who did not vote}=0.30\times \mathrm{23,252,500}=\mathrm{6,975,750}$

To convert this number into millions:
$\frac{\mathrm{6,975,750}}{\mathrm{1,000,000}}\approx 6.97575\text{ million}$

Rounding off to the nearest whole number, the approximate number of people in the electorate who did not cast their votes is 7 million.