The table displayed below represents the ratio of the count of clients enrolled in service packages for Cloud Migration to that of those registered for Database Administration across four distinct operational intervals (A, B, C, and D) at a consulting firm.
Examine the details provided in the table to address the subsequent query.
Note: Each registered client is signed up for either Cloud Migration or Database Administration, but not both.

Time slots	Ratio of employees registered for Eye checkup to Dental checkup
A	5:4
B	7:3
C	11:4
D	1:5

Assuming the total number of clients enrolled in interval C is 50% greater than the number enrolled in interval B, and given that the combined number of clients registered for Database Administration in both intervals equals 84, calculate the number of clients signed up for Cloud Migration in interval C.

The correct option is 132.

Let us break down the given information and solve the problem step-by-step.

From the table provided, the ratio of clients enrolled in Cloud Migration to Database Administration in each operational interval is as follows:
- Interval B ratio = 7 : 3
- Interval C ratio = 11 : 4

Let the total number of clients enrolled in Interval B be denoted as $T_B$, and the total number of clients in Interval C be denoted as $T_C$.

According to the problem, the total number of clients in Interval C is 50% greater than in Interval B:

$T_C=1.5\times T_B=\frac{3}{2}{T}_B$

Next, let us determine the number of clients registered for Database Administration in intervals B and C:

For Interval B, the ratio of Cloud Migration to Database Administration is 7 : 3. Thus, the fraction of clients registered for Database Administration is:

$\frac{3}{7+3}=\frac{3}{10}$

So, Database Administration clients in Interval B = $\frac{3}{10}{T}_B$.

For Interval C, the ratio of Cloud Migration to Database Administration is 11 : 4. Thus, the fraction of clients registered for Database Administration is:

$\frac{4}{11+4}=\frac{4}{15}$

So, Database Administration clients in Interval C = $\frac{4}{15}{T}_C$.

We are given that the combined number of clients registered for Database Administration in both intervals B and C equals 84:

$\frac{3}{10}{T}_B+\frac{4}{15}{T}_C=84$

Substitute $T_C=\frac{3}{2}{T}_B$ into the equation:

$\frac{3}{10}{T}_B+\frac{4}{15}\left(\frac{3}{2}{T}_B\right)=84$

Simplify the second term:

$\frac{3}{10}{T}_B+\frac{2}{5}{T}_B=84$

Convert to a common denominator (10):

$\frac{3}{10}{T}_B+\frac{4}{10}{T}_B=84$

$\frac{7}{10}{T}_B=84$

Solving for $T_B$:

$T_B=\frac{84\times 10}{7}=120$

Now calculate total clients in interval C, $T_C$:

$T_C=1.5\times 120=180$

Finally, we need to calculate the number of clients signed up for Cloud Migration in Interval C. The fraction for Cloud Migration in Interval C is $\frac{11}{15}$:

$\text{Cloud Migration clients in Interval C}=\frac{11}{15}\times 180=11\times 12=132$

Thus, the total number of clients signed up for Cloud Migration in interval C is 132.