In an election between two candidates, y% of the voters did not vote. 10% of the votes cast were declared invalid, while all the valid votes were cast in favour of either of the two candidates. The candidate who got 59.375% of the valid votes cast was declared elected by 2484 votes. If the number of people eligible to vote in that election was 16,000, what is the value of y?

The correct option is 8.

Let's break down the problem step-by-step to find the value of $y$:

First, we are given the total number of people eligible to vote in the election:
Total eligible voters = 16,000

According to the problem, $y$% of the voters did not vote. This means that the percentage of voters who did cast their votes is:
Percentage of voters who voted = $(100-y)\%$

Thus, the number of votes cast is:
$\text{Votes cast}=\mathrm{16,000}\times \frac{100-y}{100}=160(100-y)$

Next, we are told that 10% of the votes cast were declared invalid. This means 90% of the cast votes were valid. Let's calculate the total number of valid votes:
$\text{Valid votes}=90\%\text{of Votes cast}$
$\text{Valid votes}=0.9\times 160(100-y)=144(100-y)$

The winning candidate received 59.375% of the valid votes. Let's represent this percentage as a fraction to simplify calculations:
$59.375\%=\frac{59.375}{100}=\frac{59375}{100000}$
Dividing both the numerator and the denominator by 3125, we get:
$59.375\%=\frac{19}{32}$

Since all valid votes went to either of the two candidates, the losing candidate must have received the remaining share of the valid votes:
Share of losing candidate = $100\%-59.375\%=40.625\%$
In fractional form:
$40.625\%=1-\frac{19}{32}=\frac{13}{32}$

The difference in votes between the winning candidate and the losing candidate is given as 2484 votes. Let's express this difference in terms of the total valid votes:
$\text{Difference in vote share}=59.375\%-40.625\%=18.75\%$
In fractional form, this difference is:
$\frac{19}{32}-\frac{13}{32}=\frac{6}{32}=\frac{3}{16}$

So, the difference in votes is equal to $\frac{3}{16}$ of the valid votes:
$\frac{3}{16}\times \text{Valid votes}=2484$

Let's solve for the number of valid votes:
$\text{Valid votes}=2484\times \frac{16}{3}$
$\text{Valid votes}=828\times 16=\mathrm{13,248}$

Now, we equate this value to the expression for valid votes we derived earlier:
$144(100-y)=\mathrm{13,248}$

Divide both sides by 144:
$100-y=\frac{13248}{144}$
$100-y=92$

Solving for $y$:
$y=100-92$
$y=8$

Thus, the value of $y$ is 8.