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.

The correct answer is 600%.

Given Data:

From the pie chart:
Total goods manufactured by all four companies = 200
Percentage distribution of goods manufactured:
Company A = 35%
Company B = 15%
Company C = 20%
Company D = 30%

Step 1: Calculate the total goods manufactured by Company C and Company D

Total goods manufactured by Company C:
$\text{Company C}=20\%\text{of}200=\frac{20}{100}\times 200=40$

Total goods manufactured by Company D:
$\text{Company D}=30\%\text{of}200=\frac{30}{100}\times 200=60$

Step 2: Calculate the unsold goods of Company C

From the table, Company C sold 75% of its manufactured goods.
Percentage of unsold goods for Company C = 100% - 75% = 25%
Number of unsold goods for Company C:
$\text{Unsold goods of C}=25\%\text{of}40=\frac{25}{100}\times 40=10$

Step 3: Calculate the total goods manufactured by Company E

Company E manufactured 33 ¹/₃% more goods than Company D:
$33\frac{1}{3}\%=\frac{1}{3}$
Total goods manufactured by Company E:
$\text{Total manufactured by E}=60+\left(\frac{1}{3}\times 60\right)=60+20=80$

Step 4: Calculate the goods sold by Company E

The percentage of goods not sold by E is ${\left(\frac{X}{2}\right)}^{\%}$. With X = 50:
Percentage of unsold goods for Company E:
${\left(\frac{50}{2}\right)}^{\%}=25\%$
Percentage of goods sold by Company E = 100% - 25% = 75%
Number of goods sold by Company E:
$\text{Goods sold by E}=75\%\text{of}80=\frac{75}{100}\times 80=60$

Step 5: Calculate the required percentage

Percentage of goods sold by E relative to unsold goods of C:
$\text{Required Percentage}=\left(\frac{\text{Goods sold by E}}{\text{Unsold goods of C}}\right)\times 100$
$\text{Required Percentage}=\left(\frac{60}{10}\right)\times 100=600\%$

Hence, the number of goods sold by E is 600% of the unsold goods of C.