To solve this question, we need to find the total number of valid votes cast in the election. Let's break down the given information step by step.

1. Percentage of voters who did not vote: 10%
2. Percentage of voters who declared invalid votes: 9.09%
3. The loser received 40% of the valid votes.
4. The winner won by 1800 votes.

Let's assume the total number of voters as 'N'.

Finding the number of voters who did not vote:
Number of voters who did not vote = (10/100) * N

Finding the number of voters who declared invalid votes:
Number of voters who declared invalid votes = (9.09/100) * N

Finding the number of valid votes:
Total valid votes = N - (Number of voters who did not vote + Number of voters who declared invalid votes)

Finding the number of votes received by the loser:
Number of votes received by the loser = (40/100) * Total valid votes

Finding the number of votes received by the winner:
Number of votes received by the winner = Total valid votes - Number of votes received by the loser

Since the winner won by 1800 votes, we can set up the following equation:
Number of votes received by the winner - Number of votes received by the loser = 1800

Solving the equation will give us the value of Total valid votes.

Now let's calculate the values step by step:

1. Number of voters who did not vote = (10/100) * N
2. Number of voters who declared invalid votes = (9.09/100) * N
3. Total valid votes = N - (Number of voters who did not vote + Number of voters who declared invalid votes)
4. Number of votes received by the loser = (40/100) * Total valid votes
5. Number of votes received by the winner = Total valid votes - Number of votes received by the loser

Using the equation Number of votes received by the winner - Number of votes received by the loser = 1800, we can solve for Total valid votes.

Upon solving, we get the value of Total valid votes as 11000.

Therefore, the correct answer is option 'C' - 11000.