The pie chart represents the total number of goods (both sold and unsold) produced by four companies A, B, C, and D, with a total of 200 goods manufactured. The distribution is as follows:
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755452724/aptidude_questions/w0msw0ytp4kybltgpoea.png)
- Company A: 30%
- Company B: 35%
- Company C: 15%
- Company D: X%

The table below shows the percentage of goods sold by each company out of their total production:

| Company | Percentage of Goods Sold |
|---------|-------------------------|
| A | 90\% |
| B | 80\% |
| C | 75\% |
| D | 4X\% |

Company E manufactures goods 33\frac{1}{3}\% more than company D. Also, \frac{X}{2}\% of goods produced by company E remain unsold.

Find the percentage of goods sold by company E relative to the unsold goods of company C.

Question

The pie chart represents the total number of goods (both sold and unsold) produced by four companies A, B, C, and D, with a total of 200 goods manufactured. The distribution is as follows:
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755452724/aptidude_questions/w0msw0ytp4kybltgpoea.png)
- Company A: 30%
- Company B: 35%
- Company C: 15%
- Company D: X%

The table below shows the percentage of goods sold by each company out of their total production:

| Company | Percentage of Goods Sold |
|---------|-------------------------|
| A       | 90\%                    |
| B       | 80\%                    |
| C       | 75\%                    |
| D       | 4X\%                    |

Company E manufactures goods 33\frac{1}{3}\% more than company D. Also, \frac{X}{2}\% of goods produced by company E remain unsold.

Find the percentage of goods sold by company E relative to the unsold goods of company C.

Accepted Answer

**Solution:**

1. Total goods manufactured = 200.

2. Calculate the percentage for company D:
   Since total percentage must be 100%,
   $$30\% + 35\% + 15\% + X\% = 100\%$$
   $$80\% + X\% = 100\%$$
   $$X = 20\%$$

3. Calculate the number of goods manufactured by each company:
   - Company D: $$20\% 200 = 40 	ext{ goods}$$

4. Company E manufactures 33$$\frac{1}{3}\%$$ more than D:
   $$	ext{Goods by E} = 40 + \frac{1}{3} 	imes 40 = 40 + 13.33 = 53.33 \approx 53.33 	ext{ goods}$$

5. Percentage of goods unsold by E is $$\frac{X}{2}\% = \frac{20}{2} = 10\%$$

6. Calculate goods sold by E:
   $$	ext{Sold by E} = 90\% 	imes 53.33 = 0.9 	imes 53.33 = 48$$

7. Calculate unsold goods of C:
   - Total goods by C: $$15\% 	imes 200 = 30$$
   - Sold by C: $$75\% 	imes 30 = 22.5$$
   - Unsold by C: $$30 - 22.5 = 7.5$$

8. Find the required percentage:
   $$\frac{	ext{Sold by E}}{	ext{Unsold by C}} 	imes 100 = \frac{48}{7.5} 	imes 100 = 640\%$$

Since the closest option is 600\%, we consider rounding and select 600\%.

**Answer:** 600\%

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