To analyze the investment and profit division among the four individuals (A, B, C, and D), let's break this down step-by-step, including calculations and visual representation using pie charts.
Step 1: Investment Ratios
First, we need to establish the total investment and then the share for each individual based on their investment.
Investments:
- A: $30,000
- B: $40,000
- C: $60,000
- D: $70,000
Total Investment: \[ \text{Total Investment} = A + B + C + D = 30000 + 40000 + 60000 + 70000 = 200000 \]
Investment Ratios:
- A's share = \( \frac{30000}{200000} = 0.15 \) or 15%
- B's share = \( \frac{40000}{200000} = 0.20 \) or 20%
- C's share = \( \frac{60000}{200000} = 0.30 \) or 30%
- D's share = \( \frac{70000}{200000} = 0.35 \) or 35%
A. Pie Chart for Investment Ratios
To create a pie chart for the investment ratios, each individual’s percentage of total investment can be represented graphically:
- A: 15%
- B: 20%
- C: 30%
- D: 35%
This pie chart visually represents how much each person contributed to the total business investment.
Step 2: Profit Distribution
Next, we need to understand how the profits will be divided based on the agreement.
Let’s denote the total profit made by the business as \( P \).
According to their agreement:
- A, being the manager, receives one-third of the total profits: \[ \text{A's share of profit} = \frac{1}{3}P \]
The remaining profits are: \[ \text{Remaining profits} = P - \frac{1}{3}P = \frac{2}{3}P \]
These remaining profits will be divided among A, B, C, and D in proportion to their investments.
Profit Shares for B, C, and D
We need to calculate the proportions of B, C, and D based on their investment shares:
Investment Ratios for Profit Division:
-
Total Shares: 0.20 (B) + 0.30 (C) + 0.35 (D) = 0.85
-
So, if we denote \( R = \frac{2}{3}P \), the profits for each will be:
-
B's share: \[ \text{B's share of profit} = R \times 0.20 \]
-
C's share: \[ \text{C's share of profit} = R \times 0.30 \]
-
D's share: \[ \text{D's share of profit} = R \times 0.35 \]
-
Step 3: Pie Chart for Profit Distribution
Let’s assume the total profit \( P \) is $90,000 for the sake of example calculations:
-
Calculate A's share: \[ A's , share = \frac{1}{3} \times 90000 = 30000 \]
-
Calculate remaining profits: \[ Remaining , profit = 90000 - 30000 = 60000 \]
-
Distribute the remaining profit according to the ratios:
- B's share: \[ B = \frac{60000 \times 0.20}{0.85} \approx 14117.65 \]
- C's share: \[ C = \frac{60000 \times 0.30}{0.85} \approx 21176.47 \]
- D's share: \[ D = \frac{60000 \times 0.35}{0.85} \approx 24706.12 \]
So, we summarize:
- A's profit: $30,000
- B's profit: approximately $14,118
- C's profit: approximately $21,176
- D's profit: approximately $24,706
Explaining Part B
The pie chart illustrating profit distribution would visually reflect the different shares of profits based on the preceding calculations. It would show A holding a dominant slice representing his managerial fee, while the remaining three slices would be somewhat evenly sized and proportional to their investments.
- A’s slice would take up a significant portion since he receives a guaranteed one-third of profits as the manager.
- The remaining slices for B, C, and D would be smaller, reflecting their investment proportions, demonstrating that while they receive lower amounts due to the fixed managerial fee for A, their profits correlate back to their financial commitment in the business.
This approach ensures equity based on both management duty and financial investment, fulfilling the agreed terms while also aligning with fair business practices.
When creating the actual pie chart, you will use the calculated profit shares to represent each individual visually and proportionally. Each slice will be proportional to the respective profit received by A, B, C, and D.