A and B are partners sharing profits in the ratio of 3:2. C is admitted as a partner. Find out the sacrificing ratio. C is admitted as a new partner for 1/7th of his share. Calcula... A and B are partners sharing profits in the ratio of 3:2. C is admitted as a partner. Find out the sacrificing ratio. C is admitted as a new partner for 1/7th of his share. Calculate the new profit-sharing ratio.
Understand the Problem
The question is asking to calculate various ratios related to profit sharing and sacrificing among partners in a business context.
Answer
The new profit-sharing ratio is $18:12:7$.
Answer for screen readers
The sacrificing ratio for A and B is 3:2. The new profit-sharing ratio will be 18:12:7 (A:B:C).
Steps to Solve
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Identify the Original Profit-Sharing Ratio
The original profit-sharing ratio between partners A and B is given as 3:2.
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Determine Total Shares Held by Existing Partners
To find the total shares, add the shares of A and B:
$$ \text{Total Shares} = 3 + 2 = 5 $$
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Calculate C's Share
C is admitted for 1/7th of his share. Since C is acquiring a share of the total profits, we first need to determine the portion that C will receive. The share of C can be calculated as:
$$ C's\ Share = \frac{1}{7} $$
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Determine the Remaining Share for A and B
Since C now holds a portion of the profit, we need to find how much of the original profit A and B will sacrifice. The original total (5 parts) will be increased by C's share.
Since C is taking 1 part (1/7) of the total after his share is added, we calculate how much is left for A and B:
$$ Remaining = 1 - \frac{1}{7} = \frac{6}{7} $$
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Calculate the Sacrificing Ratio of A and B
The original contribution of A (3 parts) and B (2 parts) in terms of total parts is:
- A's share before = $3/5$
- B's share before = $2/5$
Thus, the sacrificing ratio can be found by calculating:
- A's sacrifice: $A_{sacrifice} = \frac{3}{5} - \frac{3}{5} \cdot \frac{1}{7}$
- B's sacrifice: $B_{sacrifice} = \frac{2}{5} - \frac{2}{5} \cdot \frac{1}{7}$
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Compute the New Shares
Apply the values derived to find the new shares:
- New A's Share = Original A's portion - A's sacrifice
- New B's Share = Original B's portion - B's sacrifice
- C becomes the new partner to share the total profits.
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Calculate the Final New Profit-Sharing Ratio
Convert the new shares into a common format to express the profit-sharing ratios clearly, and simplify if needed.
The sacrificing ratio for A and B is 3:2. The new profit-sharing ratio will be 18:12:7 (A:B:C).
More Information
In this scenario, A and B have to sacrifice portions of their profits to accommodate C into the partnership. The approach of calculating the sacrificing ratio relies on how much each partner's profits are reduced due to C's admission.
Tips
- Failing to properly calculate the remaining share after admitting a new partner.
- Not simplifying the ratios correctly after determining the new shares.
- Confusing the original shares with the new shares after sacrificing portions.
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