A customer asks for the production of x number of goods. The company produces y number of goods daily. Out of which `z%` are unfit for sale. The order will be completed in :

Options

A. `x/(100y(1-z))"days"`
B. `(100yz)/x "days"`
C. `(100x)/(y(100-z)) "days"`
D. `100/(y(z-1)) "days`

Answer

To solve the problem, we need to determine how many days it will take for the company to produce the required number of goods (X) considering that a certain percentage (z%) of the goods produced daily (Y) are unfit for sale.

### Step-by-Step Solution:

1. **Calculate the Effective Daily Production**:
The company produces Y number of goods daily, but z% of these are unfit for sale. Therefore, the effective number of goods that are fit for sale each day can be calculated as:
\[ \text{Effective Daily Production} = Y \times \left(1 - \frac{z}{100}\right) \]

2. **Determine the Total Goods Required**:
The total number of goods required is given as X.

3. **Calculate the Number of Days to Complete the Order**:
To find out how many days it will take to produce the required goods, we divide the total goods required (X) by the effective daily production:
\[ \text{Number of Days} = \frac{X}{\text{Effective Daily Production}} = \frac{X}{Y \times \left(1 - \frac{z}{100}\right)} \]

### Final Formula:
Thus, the formula to calculate the number of days required to complete the order is:
\[ \text{Number of Days} = \frac{X}{Y \times \left(1 - \frac{z}{100}\right)} \]