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

If the overall count of clients at the firm is 880 and $9\frac{1}{11}\%$ of the overall client base are enrolled in interval B, determine the difference between the clients enrolled in Database Administration and those registered for Cloud Migration within interval B.

The correct option is 32.

Step 1: Calculate the total number of clients in interval B
The overall count of clients at the firm is given as 880.
The percentage of clients enrolled in interval B is:

$9\frac{1}{11}\%=\frac{100}{11}\%=\frac{100}{11\times 100}=\frac{1}{11}$

Therefore, the total number of clients enrolled in interval B is:

$\text{Clients in interval B}=880\times \frac{1}{11}=80$

Step 2: Analyze the ratio for interval B
From the given table, the ratio of clients enrolled for Cloud Migration to Database Administration in interval B is 7 : 3.
Total ratio parts = 7 + 3 = 10 parts.

Value of 1 part:

$\text{Value of 1 part}=\frac{80}{10}=8$

Step 3: Calculate the individual counts for interval B
Number of clients in Cloud Migration (7 parts):

$7\times 8=56$

Number of clients in Database Administration (3 parts):

$3\times 8=24$

Step 4: Find the difference between the two categories
Difference between the two client counts in interval B:

$\text{Difference}=56-24=32$

Alternatively, using the ratio difference:

$\text{Difference in parts}=7-3=4\text{parts}$

$\text{Difference}=4\times 8=32$