(i) To find \(c\), use the equation for the mean: \(\frac{\Sigma x}{9} = 2205\). Therefore, \(\Sigma x = 2205 \times 9 = 19845\). Given \(\Sigma(x-c) = 1845\), we have \(\Sigma x - 9c = 1845\). Substituting \(\Sigma x = 19845\), we get:

\(19845 - 9c = 1845\)

\(9c = 19845 - 1845 = 18000\)

\(c = \frac{18000}{9} = 2000\)

(ii) The variance is given by \(\frac{\Sigma(x-c)^2}{9} - (\text{mean of } x)^2\). Substituting the given values:

Variance = \(\frac{477450}{9} - 2205^2\)

Variance = \(53050 - 2205^2\)

Variance = \(11025\)

(iii) With the new apartment, the mean becomes \(2120.50\) for 10 apartments. Therefore, the new total is:

\(2120.50 \times 10 = 21205\)

The rental price of the additional apartment is:

\(21205 - 19845 = 1360\)