Correlation coefficient:
The correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. A positive value of r indicates a positive linear relationship, while a negative value indicates a negative linear relationship. In this case, the correlation coefficient between x and y is given as 0.6, indicating a positive linear relationship.

Covariance:
Covariance measures the extent to which two variables vary together. It is calculated as the average of the product of the deviations of each data point from the mean of their respective variables. In this case, the covariance between x and y is given as 27.

Variance:
Variance measures the spread or dispersion of a variable. It is calculated as the average of the squared deviations of each data point from the mean of the variable. The variance of y is given as 25.

Formula:
The covariance between x and y can be expressed in terms of the correlation coefficient and the variances of x and y as follows:
cov(x, y) = r * σx * σy
where cov(x, y) is the covariance, r is the correlation coefficient, σx is the standard deviation of x, and σy is the standard deviation of y.

Variance of x:
We need to find the variance of x, which is denoted as Var(x).

From the formula above, we can rearrange it to solve for Var(x):
cov(x, y) = r * σx * σy
Var(x) = (cov(x, y) / (r * σy))^2

Given that cov(x, y) = 27, r = 0.6, and σy = √25 = 5, we can substitute these values into the equation to find Var(x):
Var(x) = (27 / (0.6 * 5))^2
= (27 / 3)^2
= 9^2
= 81

Therefore, the variance of x is 81, which corresponds to option 'D'.