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Sagot :
Let's break down the problem and solve it step by step to determine who is correct in this case.
### Step 1: Capitals Contributed by X and Y
First, we need to identify the amount of capital each partner contributed to the firm:
- X contributed: [tex]$100,000 - Y contributed: $[/tex]200,000
### Step 2: Total Capital in the Firm
Next, we calculate the total capital contributed to the firm by both partners:
[tex]\[ \text{Total Capital} = \text{Capital contributed by X} + \text{Capital contributed by Y} \][/tex]
[tex]\[ \text{Total Capital} = 100,000 + 200,000 = 300,000 \][/tex]
### Step 3: Ratio of Capitals
Now, we need to determine the proportion of the total capital each partner contributed.
#### Ratio of Capital X:
[tex]\[ \text{Ratio of X's Capital} = \frac{\text{Capital contributed by X}}{\text{Total Capital}} \][/tex]
[tex]\[ \text{Ratio of X's Capital} = \frac{100,000}{300,000} \approx 0.333 \][/tex]
#### Ratio of Capital Y:
[tex]\[ \text{Ratio of Y's Capital} = \frac{\text{Capital contributed by Y}}{\text{Total Capital}} \][/tex]
[tex]\[ \text{Ratio of Y's Capital} = \frac{200,000}{300,000} \approx 0.667 \][/tex]
### Step 4: Profit Distribution
Normally, in a partnership, profits are distributed according to the agreement laid out in the partnership deed. If the partnership deed specifies that profits should be distributed according to the ratio of capitals, the ratios we calculated above should be used.
Given our ratios:
- X should receive approximately 33.33% of the profits.
- Y should receive approximately 66.67% of the profits.
### Conclusion:
Y is correct if the partnership deed or agreement specifically states that the profits should be distributed based on the capital contributions. This is a standard practice in many partnerships unless there is another agreement in place that specifies a different method of profit distribution.
X's disagreement might arise from a misunderstanding or from believing that profits should be shared equally or based on some other criteria. However, without a different specific agreement in the partnership deed, the profits should indeed be distributed according to the ratio of capitals contributed by each partner.
Therefore, in the absence of any additional agreement, Y's reasoning is correct: profits should be distributed in the ratio of 33.33% to X and 66.67% to Y, reflecting their respective capital contributions.
### Step 1: Capitals Contributed by X and Y
First, we need to identify the amount of capital each partner contributed to the firm:
- X contributed: [tex]$100,000 - Y contributed: $[/tex]200,000
### Step 2: Total Capital in the Firm
Next, we calculate the total capital contributed to the firm by both partners:
[tex]\[ \text{Total Capital} = \text{Capital contributed by X} + \text{Capital contributed by Y} \][/tex]
[tex]\[ \text{Total Capital} = 100,000 + 200,000 = 300,000 \][/tex]
### Step 3: Ratio of Capitals
Now, we need to determine the proportion of the total capital each partner contributed.
#### Ratio of Capital X:
[tex]\[ \text{Ratio of X's Capital} = \frac{\text{Capital contributed by X}}{\text{Total Capital}} \][/tex]
[tex]\[ \text{Ratio of X's Capital} = \frac{100,000}{300,000} \approx 0.333 \][/tex]
#### Ratio of Capital Y:
[tex]\[ \text{Ratio of Y's Capital} = \frac{\text{Capital contributed by Y}}{\text{Total Capital}} \][/tex]
[tex]\[ \text{Ratio of Y's Capital} = \frac{200,000}{300,000} \approx 0.667 \][/tex]
### Step 4: Profit Distribution
Normally, in a partnership, profits are distributed according to the agreement laid out in the partnership deed. If the partnership deed specifies that profits should be distributed according to the ratio of capitals, the ratios we calculated above should be used.
Given our ratios:
- X should receive approximately 33.33% of the profits.
- Y should receive approximately 66.67% of the profits.
### Conclusion:
Y is correct if the partnership deed or agreement specifically states that the profits should be distributed based on the capital contributions. This is a standard practice in many partnerships unless there is another agreement in place that specifies a different method of profit distribution.
X's disagreement might arise from a misunderstanding or from believing that profits should be shared equally or based on some other criteria. However, without a different specific agreement in the partnership deed, the profits should indeed be distributed according to the ratio of capitals contributed by each partner.
Therefore, in the absence of any additional agreement, Y's reasoning is correct: profits should be distributed in the ratio of 33.33% to X and 66.67% to Y, reflecting their respective capital contributions.
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