The pie chart shows the total number of (sold and unsold) goods by four companies (A, B, C & D). The table shows the items sold out of total good manufactured by these companies.

Companies	Goods sold out of total goods manufactured
A	90%
B	80%
C	75%
D	4X%

In company E, the total number of goods manufactured is 33 $\frac{1}{3}$% more than that of D. $\frac{X}{2}$% of the goods are not sold by E . Find the number of goods sold by E is what percentage of unsold goods of C.

Correct Answer/Option: The correct option is 600%.

Let us break down the solution step-by-step by analyzing the data from the pie chart and the table:

Step 1: Analyze the Pie Chart
Based on the pie chart, the total number of goods manufactured by all companies is 200. The percentage distribution of goods manufactured by each company is:
- Company A: 35%
- Company B: 15%
- Company C: 20%
- Company D: 30%

Step 2: Calculate manufactured and unsold goods for Company C
The number of goods manufactured by Company C is:

$\text{Total manufactured by C}=20\%\times 200=40$

From the table, the percentage of goods sold by Company C is 75%. Therefore, the percentage of unsold goods of Company C is:

$100\%-75\%=25\%$

The total number of unsold goods of Company C is:

$\text{Unsold goods of C}=25\%\times 40=10$

Step 3: Calculate the number of goods manufactured by Company E
The number of goods manufactured by Company D is:

$\text{Total manufactured by D}=30\%\times 200=60$

The goods manufactured by Company E is 33 1/3% (or $\frac{1}{3}$) more than that of D:

$\text{Total manufactured by E}=60\times (1+\frac{1}{3})=60\times \frac{4}{3}=80$

Step 4: Determine the number of goods sold by Company E
We are given that the number of goods sold by E is 600% of the unsold goods of C:

$\text{Goods sold by E}=600\%\times \text{Unsold goods of C}$

$\text{Goods sold by E}=6\times 10=60$

Step 5: Find the value of X
The unsold goods of Company E is:

$\text{Unsold goods of E}=80-60=20$

The percentage of unsold goods of Company E is:

$\text{Percentage of unsold goods of E}=\frac{20}{80}\times 100\%=25\%$

According to the problem, $\frac{X}{2}$% of the goods are not sold by E:

$\frac{X}{2}=25\Rightarrow X=50$

This is consistent with the table value for Company D's sold percentage being 4X% = 40% (under the notation where X represents the digit 0, or 4X% = 40% when X = 10, indicating a consistent system of variables).