Certainly! Let's analyze and compute the various cost components step by step.
### Step 1: Calculate Prime Cost
Prime cost includes the Direct Material and Direct Labour.
[tex]\[
\text{Prime Cost} = \text{Direct Material} + \text{Direct Labour} = 4000 \text{ Rs} + 6000 \text{ Rs} = 10000 \text{ Rs}
\][/tex]
### Step 2: Calculate Factory Overheads
Factory overheads are given as 20% of the Prime Cost.
[tex]\[
\text{Factory Overheads} = \text{Prime Cost} \times 20\% = 10000 \text{ Rs} \times 0.20 = 2000 \text{ Rs}
\][/tex]
### Step 3: Calculate Works Cost
Works cost includes the Prime Cost and the Factory Overheads.
[tex]\[
\text{Works Cost} = \text{Prime Cost} + \text{Factory Overheads} = 10000 \text{ Rs} + 2000 \text{ Rs} = 12000 \text{ Rs}
\][/tex]
### Step 4: Calculate Administrative Overheads
Administrative overheads are given as 50% on Works Overheads. However, we have calculated the Factory Overheads, not the Works Overheads. Since Works Overheads are essentially the Factory Overheads, we calculate:
[tex]\[
\text{Administrative Overheads} = \text{Factory Overheads} \times 50\% = 2000 \text{ Rs} \times 0.50 = 1000 \text{ Rs}
\][/tex]
### Step 5: Calculate Cost of Production
Cost of Production includes the Works Cost and the Administrative Overheads.
[tex]\[
\text{Cost of Production} = \text{Works Cost} + \text{Administrative Overheads} = 12000 \text{ Rs} + 1000 \text{ Rs} = 13000 \text{ Rs}
\][/tex]
### Step 6: Calculate Cost of Production Per Unit
Given sales of 300 units:
[tex]\[
\text{Cost of Production Per Unit} = \frac{\text{Cost of Production}}{\text{Total Number of Units}} = \frac{13000 \text{ Rs}}{300 \text{ Units}} \approx 43.33 \text{ Rs/Unit}
\][/tex]
So, the cost of production per unit is approximately 43.33 Rs.
### Step 7: Calculate Cost of Goods Sold
Since the opening and closing stock are zero, the Cost of Goods Sold is equal to the Cost of Production:
[tex]\[
\text{Cost of Goods Sold} = \text{Cost of Production} = 13000 \text{ Rs}
\][/tex]
### Step 8: Calculate Selling and Distribution Overheads
Selling and Distribution Overheads are given as 40% of the Cost of Goods Sold.
[tex]\[
\text{Selling and Distribution Overheads} = \text{Cost of Goods Sold} \times 40\% = 13000 \text{ Rs} \times 0.40 = 5200 \text{ Rs}
\][/tex]
### Step 9: Calculate Total Cost
Total Cost includes Cost of Goods Sold and Selling & Distribution Overheads.
[tex]\[
\text{Total Cost} = \text{Cost of Goods Sold} + \text{Selling and Distribution Overheads} = 13000 \text{ Rs} + 5200 \text{ Rs} = 18200 \text{ Rs}
\][/tex]
### Step 10: Assume Sales Revenue Equals Total Cost
Here, we make an assumption that the sales revenue is equal to the total cost. Therefore, the profit per unit and the total profit can be calculated directly:
[tex]\[
\text{Total Profit} = \text{Sales Revenue} - \text{Total Cost} = 18200 \text{ Rs} - 18200 \text{ Rs} = 0 \text{ Rs}
\][/tex]
[tex]\[
\text{Profit Per Unit} = \frac{\text{Total Profit}}{\text{Total Number of Units}} = \frac{0 \text{ Rs}}{300 \text{ Units}} = 0 \text{ Rs/Unit}
\][/tex]
### Summary
(a) The cost of production per unit is approximately 43.33 Rs.
(b) The profit per unit sold is 0 Rs.
(c) The total profit for the period is 0 Rs.
This concludes our calculation and cost sheet for the given data.
