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

In company X, the total employees are average number of employees in A, C and E. The ratio of graduate employees in A and X is 1:1. Find the ratio of post graduate employees in X and graduate employees in E?

Correct Answer: 52:75

To solve this problem, we need to analyze the total number of employees from the provided bar graph along with the difference between graduate and post graduate employees from the given table.

From the problem statement, we have the following relations for any company:
1. $\text{Total Employees}=\text{Graduate}+\text{Post Graduate}$
2. $\text{Difference}=\text{Graduate}-\text{Post Graduate}$

Adding these two equations gives:
$\text{Graduate Employees}=\frac{\text{Total Employees}+\text{Difference}}{2}$

Subtracting the second equation from the first gives:
$\text{Post Graduate Employees}=\frac{\text{Total Employees}-\text{Difference}}{2}$

Step 1: Extract data for Companies A, C, and E

From the bar graph and table:
- Company A: Total employees = 220, Difference = 4
- Company C: Total employees = 224, Difference = 36
- Company E: Total employees = 204, Difference = 96

Step 2: Calculate Graduate employees in Company A

$\text{Graduate employees in A}=\frac{220+4}{2}=\frac{224}{2}=112$

Step 3: Calculate Total employees in Company X

Company X's total employees is the average number of employees in Companies A, C, and E:

$\text{Total employees in X}=\frac{220+224+204}{3}=\frac{648}{3}=216$

Step 4: Calculate Graduate and Post Graduate employees in Company X

Since the ratio of graduate employees in A and X is 1:1:

$\text{Graduate employees in X}=\text{Graduate employees in A}=112$

Now, find the post graduate employees in X:

$\text{Post graduate employees in X}=\text{Total employees in X}-\text{Graduate employees in X}$

$\text{Post graduate employees in X}=216-112=104$

Step 5: Calculate Graduate employees in Company E

$\text{Graduate employees in E}=\frac{204+96}{2}=\frac{300}{2}=150$

Step 6: Find the required ratio

Ratio of post graduate employees in X to graduate employees in E:

$\text{Ratio}=\frac{104}{150}=\frac{52}{75}$

Therefore, the required ratio is 52:75.