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 total number of clients enrolled for Cloud Migration in intervals A and D is 29 and the sum of the number of clients registered for Database Administration in these same intervals is 40, then calculate the difference between the total number of clients in interval A and interval D.

The correct option is 21.

Step-by-Step Explanation:

1. Understand the Ratios for Intervals A and D:

From the table provided, the ratio of clients enrolled in Cloud Migration to Database Administration is:

- For Interval A: 5 : 4

- For Interval D: 1 : 5

Let the multiplier for interval A be $x$ and for interval D be $y$.

This gives us the following counts:

- Interval A: Cloud Migration = $5x$, Database Administration = $4x$

- Interval D: Cloud Migration = $1y$, Database Administration = $5y$

2. Formulate Equations from the Given Conditions:

Condition 1: Total clients enrolled for Cloud Migration in intervals A and D is 29.

$5x+y=29$     --- (Equation 1)

Condition 2: Total clients registered for Database Administration in intervals A and D is 40.

$4x+5y=40$     --- (Equation 2)

3. Solve the System of Linear Equations:

From Equation 1, express $y$ in terms of $x$:

$y=29-5x$

Substitute $y$ into Equation 2:

$4x+5(29-5x)=40$

$4x+145-25x=40$

$-21x=40-145$

$-21x=-105$

$x=5$

Now substitute $x=5$ back to find $y$:

$y=29-5\left(5\right)=29-25=4$

4. Calculate Total Clients in Interval A and Interval D:

- Total clients in Interval A = $5x+4x=9x=9\times 5=45$

- Total clients in Interval D = $1y+5y=6y=6\times 4=24$

5. Find the Difference:

Difference = Total clients in Interval A - Total clients in Interval D

$\text{Difference}=45-24=21$

Thus, the difference between the total number of clients in interval A and interval D is 21.