Bar graph given below shows the total number of graduate and post graduate employees in five different companies. Table shows the difference between graduate and posts graduate employees.

Companies	Graduate – Post Graduate employees
A	4
B	2
C	36
D	90
E	96

Note – Total Employees = Graduate + Post Graduate Employees
Graduate employees are more than Post Graduate Employees

Find the difference between average number of graduate employees in B and D and average number of post graduate employees in A and E?

Correct Answer: The correct answer is 41.

Step-by-Step Explanation:

From the given bar graph, the total number of employees (Graduate + Post Graduate) for each company is:

• Company A = 220
• Company B = 195
• Company C = 225
• Company D = 200
• Company E = 205

From the given table, the difference between Graduate and Post Graduate employees (Graduate - Post Graduate) for each company is:

• Company A = 4
• Company B = 2
• Company C = 36
• Company D = 90
• Company E = 96

Using the given conditions:

$\text{Total Employees}=\text{Graduate}+\text{Post Graduate}$

$\text{Difference}=\text{Graduate}-\text{Post Graduate}$

We can derive the individual formulas for Graduate and Post Graduate employees:

$\text{Graduate Employees}=\frac{\text{Total}+\text{Difference}}{2}$

$\text{Post Graduate Employees}=\frac{\text{Total}-\text{Difference}}{2}$

Step 1: Calculate Graduate employees in B and D

Graduate employees in B:

$\text{Graduate (B)}=\frac{195+2}{2}=\frac{197}{2}=98.5$

Graduate employees in D:

$\text{Graduate (D)}=\frac{200+90}{2}=\frac{290}{2}=145$

Average number of graduate employees in B and D:

$\text{Average Graduate (B, D)}=\frac{98.5+145}{2}=\frac{243.5}{2}=121.75$

Step 2: Calculate Post Graduate employees in A and E

Post Graduate employees in A:

$\text{Post Graduate (A)}=\frac{220-4}{2}=\frac{216}{2}=108$

Post Graduate employees in E:

$\text{Post Graduate (E)}=\frac{205-96}{2}=\frac{109}{2}=54.5$

Average number of post graduate employees in A and E:

$\text{Average Post Graduate (A, E)}=\frac{108+54.5}{2}=\frac{162.5}{2}=81.25$

Step 3: Find the difference between the two averages

$\text{Required Difference}=121.75-81.25=40.5\approx 41$

Rounding 40.5 to the nearest whole integer gives 41.