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Sagot :
To solve the problem, we need to identify and calculate the missing values and percentages for the three businesses based on the accounting information provided. Let’s go through each business step-by-step:
### Business A Calculations:
1. Purchases (A):
[tex]\[ \text{Cost of goods available for sale} = \text{Opening Stock} + \text{Purchases} + \text{Carriage on Purchases} \][/tex]
[tex]\[ 198000 = 66000 + \text{Purchases} + 8000 \][/tex]
[tex]\[ \text{Purchases} = 198000 - 66000 - 8000 = 124000 \][/tex]
2. Cost of Sales:
[tex]\[ \text{Cost of Sales} = \text{Cost of Goods Available for Sale} - \text{Closing Stock} \][/tex]
[tex]\[ \text{Cost of Sales} = 198000 - 85000 = 113000 \][/tex]
3. Gross Profit:
[tex]\[ \text{Gross Profit} = \text{Sales} - \text{Cost of Sales} \][/tex]
[tex]\[ \text{Gross Profit} = 214500 - 113000 = 101500 \][/tex]
4. 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]\[ \text{Gross Profit on Cost of Sales} = \frac{101500}{113000} \approx 0.8982 \text{ or } 89.82\% \][/tex]
5. Gross Profit on Turnover:
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ \text{Gross Profit on Turnover} = \frac{101500}{214500} \approx 0.473 \text{ or } 47.3\% \][/tex]
### Business B Calculations:
1. Sales (F):
[tex]\[ \text{Sales} = \text{Gross Profit} + \text{Cost of Sales} \][/tex]
[tex]\[ \text{Sales} = 54200 + 135500 = 189700 \][/tex]
2. Gross Profit on Turnover (G):
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ \text{Gross Profit on Turnover} = \frac{54200}{189700} \approx 0.2857 \text{ or } 28.57\% \][/tex]
### Business C Calculations:
1. Purchases:
We don't need to calculate anything here as there's no information.
2. Carriage on Purchases:
We don't need to calculate anything here as there's no information.
3. Closing Stock:
We don't need to calculate anything here as there's no information.
4. Cost of Sales:
Given as 130000
5. Gross Profit:
We don't need to calculate anything here as there's no information.
6. Sales:
Given as 200000
7. Gross Profit on Cost of Sales (K):
[tex]\[ \frac{\text{Gross Profit}}{\text{Cost of Sales}} = \text{Gross Profit on Cost of Sales} \][/tex]
8. Gross Profit on Turnover (L):
We don't have sufficient data here.
Summarizing all our results:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Balance Totals (20 February 2021)} & \text{Business A} & \text{Business B} & \text{Business C} \\ \hline \text{Opening Stock} & 66000 & 56000 & 115000 \\ \hline \text{Purchases} & 124000 & 20000 & - \\ \hline \text{Carriage on Purchases} & 8000 & 7500 & - \\ \hline \text{Cost of Goods Available for Sales} & 198000 & - & 169000 \\ \hline \text{Less Closing Stock} & 85000 & - & - \\ \hline \text{Cost of Sales} & 113000 & 135500 & 130000 \\ \hline \text{Gross Profit} & 101500 & 54200 & - \\ \hline \text{Sales} & 214500 & 189700 & 200000 \\ \hline \text{Gross Profit on Cost of Sales (\%)} & 89.82\% & 40\% & - \\ \hline \text{Gross Profit on Turnover (\%)} & 47.3\% & 28.57\% & - \\ \hline \end{array} \][/tex]
### Business A Calculations:
1. Purchases (A):
[tex]\[ \text{Cost of goods available for sale} = \text{Opening Stock} + \text{Purchases} + \text{Carriage on Purchases} \][/tex]
[tex]\[ 198000 = 66000 + \text{Purchases} + 8000 \][/tex]
[tex]\[ \text{Purchases} = 198000 - 66000 - 8000 = 124000 \][/tex]
2. Cost of Sales:
[tex]\[ \text{Cost of Sales} = \text{Cost of Goods Available for Sale} - \text{Closing Stock} \][/tex]
[tex]\[ \text{Cost of Sales} = 198000 - 85000 = 113000 \][/tex]
3. Gross Profit:
[tex]\[ \text{Gross Profit} = \text{Sales} - \text{Cost of Sales} \][/tex]
[tex]\[ \text{Gross Profit} = 214500 - 113000 = 101500 \][/tex]
4. 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]\[ \text{Gross Profit on Cost of Sales} = \frac{101500}{113000} \approx 0.8982 \text{ or } 89.82\% \][/tex]
5. Gross Profit on Turnover:
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ \text{Gross Profit on Turnover} = \frac{101500}{214500} \approx 0.473 \text{ or } 47.3\% \][/tex]
### Business B Calculations:
1. Sales (F):
[tex]\[ \text{Sales} = \text{Gross Profit} + \text{Cost of Sales} \][/tex]
[tex]\[ \text{Sales} = 54200 + 135500 = 189700 \][/tex]
2. Gross Profit on Turnover (G):
[tex]\[ \text{Gross Profit on Turnover} = \frac{\text{Gross Profit}}{\text{Sales}} \][/tex]
[tex]\[ \text{Gross Profit on Turnover} = \frac{54200}{189700} \approx 0.2857 \text{ or } 28.57\% \][/tex]
### Business C Calculations:
1. Purchases:
We don't need to calculate anything here as there's no information.
2. Carriage on Purchases:
We don't need to calculate anything here as there's no information.
3. Closing Stock:
We don't need to calculate anything here as there's no information.
4. Cost of Sales:
Given as 130000
5. Gross Profit:
We don't need to calculate anything here as there's no information.
6. Sales:
Given as 200000
7. Gross Profit on Cost of Sales (K):
[tex]\[ \frac{\text{Gross Profit}}{\text{Cost of Sales}} = \text{Gross Profit on Cost of Sales} \][/tex]
8. Gross Profit on Turnover (L):
We don't have sufficient data here.
Summarizing all our results:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Balance Totals (20 February 2021)} & \text{Business A} & \text{Business B} & \text{Business C} \\ \hline \text{Opening Stock} & 66000 & 56000 & 115000 \\ \hline \text{Purchases} & 124000 & 20000 & - \\ \hline \text{Carriage on Purchases} & 8000 & 7500 & - \\ \hline \text{Cost of Goods Available for Sales} & 198000 & - & 169000 \\ \hline \text{Less Closing Stock} & 85000 & - & - \\ \hline \text{Cost of Sales} & 113000 & 135500 & 130000 \\ \hline \text{Gross Profit} & 101500 & 54200 & - \\ \hline \text{Sales} & 214500 & 189700 & 200000 \\ \hline \text{Gross Profit on Cost of Sales (\%)} & 89.82\% & 40\% & - \\ \hline \text{Gross Profit on Turnover (\%)} & 47.3\% & 28.57\% & - \\ \hline \end{array} \][/tex]
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