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Sagot :
To solve for all the unknown amounts and percentages, we need to systematically apply the relevant accounting formulas and relationships. Below is the detailed step-by-step process for each business.
### Business A:
1. Cost of Sales (B):
[tex]\[ \text{Cost of Sales} = \text{Cost of Goods Available for Sale} - \text{Closing Stock} \][/tex]
[tex]\[ B = 198,000 - 55,000 \][/tex]
[tex]\[ B = 143,000 \][/tex]
2. Gross Profit on Cost of Sales (C):
[tex]\[ \text{Gross Profit on Cost of Sales} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \][/tex]
[tex]\[ C = \frac{71,500}{143,000} \][/tex]
[tex]\[ C \approx 0.50 \text{ or } 50\% \][/tex]
3. Purchases (A):
[tex]\[ \text{Cost of Goods Available for Sale} = \text{Opening Stock} + \text{Purchases} + \text{Carriage on Purchases} \][/tex]
[tex]\[ 198,000 = 60,000 + A + 8,000 \][/tex]
[tex]\[ A = 198,000 - 68,000 \][/tex]
[tex]\[ A = 130,000 \][/tex]
### Business B:
4. Cost of Goods Available for Sale (D):
[tex]\[ \text{Cost of Goods Available for Sale} = \text{Opening Stock} + \text{Purchases} + \text{Carriage on Purchases} \][/tex]
[tex]\[ D = 56,000 + 120,000 + 7,500 \][/tex]
[tex]\[ D = 183,500 \][/tex]
5. Closing Stock (E):
[tex]\[ \text{Cost of Sales} = \text{Cost of Goods Available for Sale} - \text{Closing Stock} \][/tex]
[tex]\[ 135,500 = 183,500 - E \][/tex]
[tex]\[ E = 183,500 - 135,500 \][/tex]
[tex]\[ E = 48,000 \][/tex]
6. Sales (F):
[tex]\[ \text{Sales} = \text{Gross Profit} + \text{Cost of Sales} \][/tex]
[tex]\[ F = 54,200 + 135,500 \][/tex]
[tex]\[ F = 189,700 \][/tex]
7. Gross Profit on Cost of Sales (W):
[tex]\[ \text{Gross Profit on Cost of Sales} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \][/tex]
[tex]\[ W = \frac{54,200}{135,500} \][/tex]
[tex]\[ W \approx 0.40 \text{ or } 40\% \][/tex]
8. Gross Profit on Turnover (G):
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ G = \frac{54,200}{189,700} \][/tex]
[tex]\[ G \approx 0.2856 \text{ or } 28.56\% \][/tex]
### Business C:
9. Gross Profit (J):
[tex]\[ \text{Gross Profit} = \text{Sales} - \text{Cost of Sales} \][/tex]
[tex]\[ J = 208,000 - 130,000 \][/tex]
[tex]\[ J = 78,000 \][/tex]
10. Closing Stock (I):
[tex]\[ \text{Cost of Goods Available for Sale} = \text{Cost of Sales} + \text{Closing Stock} \][/tex]
[tex]\[ 169,000 - I = 130,000 \][/tex]
[tex]\[ I = 169,000 - 130,000 \][/tex]
[tex]\[ I = 39,000 \][/tex]
11. Gross Profit on Cost of Sales (K):
[tex]\[ \text{Gross Profit on Cost of Sales} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \][/tex]
[tex]\[ K = \frac{78,000}{130,000} \][/tex]
[tex]\[ K \approx 0.60 \text{ or } 60\% \][/tex]
12. Gross Profit on Turnover (L):
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ L = \frac{78,000}{208,000} \][/tex]
[tex]\[ L \approx 0.375 \text{ or } 37.5\% \][/tex]
### Summary of Solutions:
- Business A:
- [tex]\( A = 130,000 \)[/tex]
- [tex]\( B = 143,000 \)[/tex]
- [tex]\( C = 50\% \)[/tex]
- Business B:
- [tex]\( D = 183,500 \)[/tex]
- [tex]\( E = 48,000 \)[/tex]
- [tex]\( F = 189,700 \)[/tex]
- [tex]\( W = 40\% \)[/tex]
- [tex]\( G = 28.56\% \)[/tex]
- Business C:
- [tex]\( H = (\text{Calculated implicitly in known values})\)[/tex]
- [tex]\( I = 39,000 \)[/tex]
- [tex]\( J = 78,000 \)[/tex]
- [tex]\( K = 60\% \)[/tex]
- [tex]\( L = 37.5\% \)[/tex]
Each calculation follows standard accounting practices for determining the cost of goods sold, gross profit, and related ratios.
### Business A:
1. Cost of Sales (B):
[tex]\[ \text{Cost of Sales} = \text{Cost of Goods Available for Sale} - \text{Closing Stock} \][/tex]
[tex]\[ B = 198,000 - 55,000 \][/tex]
[tex]\[ B = 143,000 \][/tex]
2. Gross Profit on Cost of Sales (C):
[tex]\[ \text{Gross Profit on Cost of Sales} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \][/tex]
[tex]\[ C = \frac{71,500}{143,000} \][/tex]
[tex]\[ C \approx 0.50 \text{ or } 50\% \][/tex]
3. Purchases (A):
[tex]\[ \text{Cost of Goods Available for Sale} = \text{Opening Stock} + \text{Purchases} + \text{Carriage on Purchases} \][/tex]
[tex]\[ 198,000 = 60,000 + A + 8,000 \][/tex]
[tex]\[ A = 198,000 - 68,000 \][/tex]
[tex]\[ A = 130,000 \][/tex]
### Business B:
4. Cost of Goods Available for Sale (D):
[tex]\[ \text{Cost of Goods Available for Sale} = \text{Opening Stock} + \text{Purchases} + \text{Carriage on Purchases} \][/tex]
[tex]\[ D = 56,000 + 120,000 + 7,500 \][/tex]
[tex]\[ D = 183,500 \][/tex]
5. Closing Stock (E):
[tex]\[ \text{Cost of Sales} = \text{Cost of Goods Available for Sale} - \text{Closing Stock} \][/tex]
[tex]\[ 135,500 = 183,500 - E \][/tex]
[tex]\[ E = 183,500 - 135,500 \][/tex]
[tex]\[ E = 48,000 \][/tex]
6. Sales (F):
[tex]\[ \text{Sales} = \text{Gross Profit} + \text{Cost of Sales} \][/tex]
[tex]\[ F = 54,200 + 135,500 \][/tex]
[tex]\[ F = 189,700 \][/tex]
7. Gross Profit on Cost of Sales (W):
[tex]\[ \text{Gross Profit on Cost of Sales} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \][/tex]
[tex]\[ W = \frac{54,200}{135,500} \][/tex]
[tex]\[ W \approx 0.40 \text{ or } 40\% \][/tex]
8. Gross Profit on Turnover (G):
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ G = \frac{54,200}{189,700} \][/tex]
[tex]\[ G \approx 0.2856 \text{ or } 28.56\% \][/tex]
### Business C:
9. Gross Profit (J):
[tex]\[ \text{Gross Profit} = \text{Sales} - \text{Cost of Sales} \][/tex]
[tex]\[ J = 208,000 - 130,000 \][/tex]
[tex]\[ J = 78,000 \][/tex]
10. Closing Stock (I):
[tex]\[ \text{Cost of Goods Available for Sale} = \text{Cost of Sales} + \text{Closing Stock} \][/tex]
[tex]\[ 169,000 - I = 130,000 \][/tex]
[tex]\[ I = 169,000 - 130,000 \][/tex]
[tex]\[ I = 39,000 \][/tex]
11. Gross Profit on Cost of Sales (K):
[tex]\[ \text{Gross Profit on Cost of Sales} = \frac{\text{Gross Profit}}{\text{Cost of Sales}} \][/tex]
[tex]\[ K = \frac{78,000}{130,000} \][/tex]
[tex]\[ K \approx 0.60 \text{ or } 60\% \][/tex]
12. Gross Profit on Turnover (L):
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ L = \frac{78,000}{208,000} \][/tex]
[tex]\[ L \approx 0.375 \text{ or } 37.5\% \][/tex]
### Summary of Solutions:
- Business A:
- [tex]\( A = 130,000 \)[/tex]
- [tex]\( B = 143,000 \)[/tex]
- [tex]\( C = 50\% \)[/tex]
- Business B:
- [tex]\( D = 183,500 \)[/tex]
- [tex]\( E = 48,000 \)[/tex]
- [tex]\( F = 189,700 \)[/tex]
- [tex]\( W = 40\% \)[/tex]
- [tex]\( G = 28.56\% \)[/tex]
- Business C:
- [tex]\( H = (\text{Calculated implicitly in known values})\)[/tex]
- [tex]\( I = 39,000 \)[/tex]
- [tex]\( J = 78,000 \)[/tex]
- [tex]\( K = 60\% \)[/tex]
- [tex]\( L = 37.5\% \)[/tex]
Each calculation follows standard accounting practices for determining the cost of goods sold, gross profit, and related ratios.
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