In an election between two candidates, 10% of the registered voters did not cast their vote. The winning candidate got 60% of the total votes cast and defeated the other candidate by 1242 votes. Find the total number of registered voters.

The correct answer is 6900.

Step-by-Step Explanation:

Let the total number of registered voters be $x$.

Step 1: Calculate the total number of votes cast.
It is given that 10% of the registered voters did not cast their vote.
Percentage of voters who cast their vote = $100\%-10\%=90\%$
Therefore, the total votes cast = $90\%$ of $x=0.9x$.

Step 2: Find the percentage of votes obtained by each candidate.
The winning candidate got 60% of the total votes cast.
Therefore, the losing candidate got $100\%-60\%=40\%$ of the total votes cast.

Step 3: Calculate the difference in votes between the winning and losing candidates.
Difference in percentage of total votes cast = $60\%-40\%=20\%$ of total votes cast.
So, the margin of victory in votes = $20\%$ of $0.9x$
$=0.20\times 0.9x=0.18x$.

Step 4: Equate to the given winning margin and solve for $x$.
Given that the winning candidate defeated the other candidate by 1242 votes:
$0.18x=1242$

$x=\frac{1242}{0.18}$

$x=\frac{124200}{18}$

$x=6900$

Thus, the total number of registered voters is 6900.