Out of the shirts produced in a factory `15%` are defective, while `20%` of rest are sold in domestic market. If the remaining `8840` shirts are left for expart then the number of shirts produced in the factory is ?

Options

A. Rs. `16,000`
B. Rs. `14,000`
C. Rs. `16,500`
D. Rs. `13,000`

Answer

To find the total number of shirts produced in the factory, we can follow these steps:

### Step 1: Define the total number of shirts produced
Let the total number of shirts produced in the factory be represented by \( x \).

### Step 2: Calculate the number of defective shirts
Since 15% of the shirts are defective, the number of defective shirts can be calculated as:
\[ \text{Defective shirts} = 15\% \text{ of } x = \frac{15}{100} \times x = 0.15x \]

### Step 3: Calculate the number of non-defective shirts
The number of non-defective shirts is the total shirts minus the defective shirts:
\[ \text{Non-defective shirts} = x - 0.15x = 0.85x \]

### Step 4: Calculate the number of shirts sold in the domestic market
20% of the non-defective shirts are sold in the domestic market:
\[ \text{Shirts sold domestically} = 20\% \text{ of } 0.85x = \frac{20}{100} \times 0.85x = 0.17x \]

### Step 5: Calculate the remaining shirts for export
The remaining shirts after selling some domestically are:
\[ \text{Remaining shirts for export} = \text{Non-defective shirts} - \text{Shirts sold domestically} = 0.85x - 0.17x = 0.68x \]

### Step 6: Set up the equation with the remaining shirts
According to the problem, the remaining shirts for export amount to 8840:
\[ 0.68x = 8840 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides of the equation by 0.68:
\[ x = \frac{8840}{0.68} \]
Calculating this gives:
\[ x = 13000 \]

### Conclusion
The total number of shirts produced in the factory is \( 13000 \).

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