A and B are partners sharing profit in the ratio of 5:3. C is admitted to the partnership for 1/4th share of future profits. Calculate the new profit sharing ratio. New profit shar... A and B are partners sharing profit in the ratio of 5:3. C is admitted to the partnership for 1/4th share of future profits. Calculate the new profit sharing ratio. New profit sharing ratio A:B:C = 15:9:8. P and Q are partners. P gets 60% and Q gets 40% of profits. R is admitted for 20 paise in a rupee. Find the sacrifice ratio.
Understand the Problem
The question is asking for the calculation of a new profit sharing ratio and sacrifice ratio in a partnership setting where certain partners are admitted and existing shares are adjusted. The details provided outline the original sharing ratios and the conditions for new shares being allocated, specifically for partners A, B, and C, as well as for partners P and Q.
Answer
The new profit sharing ratio is $A : B : C = 2 : 1 : 1$.
Answer for screen readers
The new profit sharing ratio is $A : B : C = 2 : 1 : 1$.
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 $5 : 3$.
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Convert the original ratios to a common format To make calculations easier, convert the sharing ratios to fractions:
- A's share = $\frac{5}{8}$ (since $5 + 3 = 8$)
- B's share = $\frac{3}{8}$
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Determine the new share for C Partner C is admitted for a $\frac{1}{4}$ share. To integrate this into the total share:
- C’s share = $\frac{1}{4} = \frac{2}{8}$ (convert to out of 8)
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Calculate the remaining share The total share so far is $A + B + C = \frac{5}{8} + \frac{3}{8} + \frac{2}{8} = 1$. This means the total distribution is accurate with no remainder.
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Adjust the ratios of A and B C’s admission means A and B need to sacrifice parts of their shares. The sacrifice by each is based on their original shares:
- Sacrifice from A = Original share (A) portion assigned to C: $\frac{1}{4}$ = $\frac{2}{8} \Rightarrow $ A sacrifices $ \frac{1}{8}$
- Sacrifice from B = B’s remaining share to accommodate C = Sacrifice from A + B = $\frac{2}{8} + \frac{1}{8} = \frac{3}{8}$
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Calculate the new shares for A, B, and C
- New share for A = $\frac{5}{8} - \frac{1}{8} = \frac{4}{8} = \frac{1}{2}$
- New share for B = $\frac{3}{8} - \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$
- New share for C = $\frac{1}{4} = \frac{2}{8}$
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New profit sharing ratio Combine the new shares A, B, and C:
- A : B : C = $\frac{4}{8} : \frac{2}{8} : \frac{2}{8} = 4 : 2 : 2 = 2 : 1 : 1$
The new profit sharing ratio is $A : B : C = 2 : 1 : 1$.
More Information
The new profit-sharing ratios reflect the contributions and sacrifices made by the original partners when admitting C into the partnership.
Tips
- Forgetting to convert shares into a common denominator when calculating sacrifices can lead to incorrect results. Always ensure shares are out of the same total values.
- Not accounting for each partner’s sacrifice accurately. It’s important to track how much of their profit share each partner gives up.
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