To solve this problem, we will first calculate the total investment made by D, E, and F and then find their individual shares in the profit of $4500 based on their respective investment proportions.

Step 1: Total investment

D's investment: $4000
E's investment: $6000
F's investment: $5000

Total investment = $4000 + 6000 + 5000 = 15000$

Step 2: Proportional share

Each person's share of the profit is proportional to their investment. Let us calculate the fraction of the total investment for each person.

• D's proportion = $\frac{4000}{15000} = \frac{4}{15}$
• E's proportion = $\frac{6000}{15000} = \frac{6}{15} = \frac{2}{5}$
• F's proportion = $\frac{5000}{15000} = \frac{5}{15} = \frac{1}{3}$

Step 3: Share of the profit

Now, multiply each proportion by the total profit of $4500.

• D's share = $\frac{4}{15} \times 4500 = 1200$
• E's share = $\frac{2}{5} \times 4500 = 1800$
• F's share = $\frac{1}{3} \times 4500 = 1500$

Final Answer:

• D receives $1200
• E receives $1800
• F receives $1500

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Do you want a detailed explanation of the proportional method or further clarifications?

Related Questions:

1. How is the profit-sharing ratio derived from investments?
2. What if the total profit changes? How do the shares adjust?
3. How would the calculation differ if one partner reinvests profits back into the business?
4. What is the implication of unequal profit sharing in partnerships?
5. Can the concept be extended to include a fourth partner? How?

Tip:

When calculating proportional shares, always confirm the sum of individual shares equals the total profit to verify your calculation.