The table below provides details regarding the number of men and women working at five distinct corporations (V, W, X, Y, and Z), along with the proportion of total personnel (men + women) who received a promotion at each corporation. Review the dataset to answer the question that follows.

Corporation	Men	Women	% of personnel promoted
V	400	350	40%
W	260	100	80%
X	340	410	60%
Y	200	300	80%
Z	240	360	50%

Note: The total staff size at any corporation is the sum of the men and women working there.

Determine the ratio of the promoted personnel in X and Z combined to the average number of staff members in V and Y.

The correct option is 6 : 5.

Let us calculate the required values step-by-step from the given table dataset.

Step 1: Calculate total staff members in each corporation

The total staff size at any corporation is the sum of men and women working there.

For Corporation V:
Total Staff = 400 + 350 = 750

For Corporation X:
Total Staff = 340 + 410 = 750

For Corporation Y:
Total Staff = 200 + 300 = 500

For Corporation Z:
Total Staff = 240 + 360 = 600

Step 2: Calculate the number of promoted personnel in X and Z

In Corporation X:
Promoted percentage = 60%
Number of promoted personnel in X = 60% of 750

$=\frac{60}{100}\times 750=450$

In Corporation Z:
Promoted percentage = 50%
Number of promoted personnel in Z = 50% of 600

$=\frac{50}{100}\times 600=300$

Total promoted personnel in X and Z combined = 450 + 300 = 750.

Step 3: Calculate the average number of staff members in V and Y

Total staff in V = 750
Total staff in Y = 500

Average number of staff members in V and Y:

$=\frac{750+500}{2}=\frac{1250}{2}=625$

Step 4: Find the required ratio

Ratio of promoted personnel in X and Z combined to the average staff in V and Y:

$=\frac{750}{625}$

Dividing both the numerator and the denominator by 125:

$=\frac{6}{5}$

Thus, the required ratio is 6 : 5.