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 answer is 32.

Let's break down the solution step-by-step to find the required difference in interval B.

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

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

So, the total number of clients in interval B is:

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

Step 2: Determine the ratio of clients for Cloud Migration and Database Administration in interval B.
From the given table, for interval B, the ratio of clients enrolled in the two services (Cloud Migration : Database Administration) is 7 : 3.
Total ratio parts = 7 + 3 = 10 parts.

Step 3: Calculate the number of clients in each service for interval B.
Value of 1 part:

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

Number of clients registered for Cloud Migration in interval B:

$7\times 8=56$

Number of clients registered for Database Administration in interval B:

$3\times 8=24$

Step 4: Find the difference between the clients in Database Administration and Cloud Migration within interval B.
Difference = 56 - 24 = 32 (or using ratio parts, difference = (7 - 3) parts = 4 parts, which is 4 × 8 = 32).

Thus, the difference between the clients enrolled in Database Administration and Cloud Migration in interval B is 32.