To draw pie charts representing the investments and the profit distribution of A, B, C, and D, let's start by calculating the necessary values step by step.
A. Investment Ratios
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Total Investment: \[ \text{Total Investment} = A + B + C + D = 30000 + 40000 + 60000 + 70000 = 200000 \]
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Individual Investment Ratios:
- A's Ratio: \( \frac{30000}{200000} = 0.15 \) (15%)
- B's Ratio: \( \frac{40000}{200000} = 0.20 \) (20%)
- C's Ratio: \( \frac{60000}{200000} = 0.30 \) (30%)
- D's Ratio: \( \frac{70000}{200000} = 0.35 \) (35%)
Pie Chart for Investments
In a pie chart, each section will represent the proportion of each person's investment:
- A: 15%
- B: 20%
- C: 30%
- D: 35%
B. Profit Distribution
Let's assume the total profit for the business is \(P\).
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Manager’s Share: A receives one-third of the total profit: \[ A's \text{ Share} = \frac{1}{3}P \]
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Remaining Profit: \[ \text{Remaining Profit} = P - A's \text{ Share} = P - \frac{1}{3}P = \frac{2}{3}P \]
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Distribution of Remaining Profit Among A, B, C, and D: The remaining profit is divided in proportion to their investments. The total investment proportion was already calculated, so we will use these ratios to divide the remaining profit.
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Proportional Shares of Remaining Profit: Let \(X\) be the total amount (in terms of profit) distributed among A, B, C, and D based on their investments.
- Total ratio of just the investments (without A's share): 20% (B) + 30% (C) + 35% (D) = 85%
- The shares out of remaining profit:
- B's Share of Remaining Profit: \( \frac{40000}{200000} \times \frac{2}{3}P = \frac{2}{3} \times 0.20P = \frac{2}{15}P \)
- C's Share of Remaining Profit: \( \frac{60000}{200000} \times \frac{2}{3}P = \frac{2}{3} \times 0.30P = \frac{1}{5}P \)
- D's Share of Remaining Profit: \( \frac{70000}{200000} \times \frac{2}{3}P = \frac{2}{3} \times 0.35P = \frac{7}{30}P \)
Putting together all shares:
- A's total share = \(\frac{1}{3}P + \frac{2}{15}P\)
- B's total share = \(\frac{2}{15}P\)
- C's total share = \(\frac{1}{5}P = \frac{3}{15}P\)
- D's total share = \(\frac{7}{30}P = \frac{14}{60}P = \frac{7}{30}P\)
Pie Chart for Profit Distribution
Now, let's summarize:
- A's total share = \(\frac{1}{3}P + \frac{2}{15}P\)
- B's share = \(\frac{2}{15}P\)
- C's share = \(\frac{3}{15}P\)
- D's share = \(\frac{14}{60}P\)
The representation in percentages based on \(P\):
- A's Share: Total of A's share will be \( (A's \text{ share from profit}) = 33.33 + 13.33 = 46.67% \)
- B's Share: 13.33%
- C's Share: 20%
- D's Share: 23.33%
Drawing the Pie Charts
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For the investment pie chart, you would have:
- A (15%)
- B (20%)
- C (30%)
- D (35%)
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For the profit distribution pie chart, you would have:
- A (46.67%)
- B (13.33%)
- C (20%)
- D (23.33%)
You can use graphing software or tools to create these pie charts based on the proportions above. If you do this manually, the percentages will map directly to angles: \(360 \times \text{percentage}\).