Formula for Sacrifice Ratio

Oct 13, 2025 by pynkocean.com 121 views

Rajesh and Rakesh are partners sharing profits and losses in ratio of 5:3. They admit Ramesh as a new partner. The new profit sharing ratio is 3:2:1 respectively Find out the sacrifice ratio of old partners.

In a partnership firm, the partners share profits and losses in a predetermined ratio. When a new partner is admitted into the firm, the existing partners may have to sacrifice some of their share in the profits and losses. This sacrifice ratio is an important concept in partnership accounting, as it helps to determine the amount of sacrifice made by the old partners. In this article, we will discuss how to find the sacrifice ratio of old partners when a new partner is admitted into the firm.

The sacrifice ratio is the ratio of the difference between the old profit-sharing ratio and the new profit-sharing ratio. It is calculated by finding the difference between the old and new profit-sharing ratios and then dividing it by the old profit-sharing ratio.

Formula for Sacrifice Ratio

The formula for sacrifice ratio is as follows:

Sacrifice Ratio = (Old Profit-Sharing Ratio - New Profit-Sharing Ratio) / Old Profit-Sharing Ratio

Example

Let's consider an example to illustrate how to find the sacrifice ratio of old partners.

Rajesh and Rakesh are partners sharing profits and losses in a ratio of 5:3. They admit Ramesh as a new partner. The new profit-sharing ratio is 3:2:1 respectively.

Step 1: Calculate the Old Profit-Sharing Ratio

The old profit-sharing ratio is 5:3, which can be written as 5x:3x, where x is a common factor.

Step 2: Calculate the New Profit-Sharing Ratio

The new profit-sharing ratio is 3:2:1, which can be written as 3y:2y:1y, where y is a common factor.

Step 3: Find the Difference between the Old and New Profit-Sharing Ratios

To find the difference between the old and new profit-sharing ratios, we need to find the difference between the two ratios.

Old Profit-Sharing Ratio = 5x:3x New Profit-Sharing Ratio = 3y:2y:1y

The difference between the old and new profit-sharing ratios is:

(5x - 3y) : (3x - 2y) : (x - y)

Step 4: Calculate the Sacrifice Ratio

Now, we can calculate the sacrifice ratio using the formula:

Sacrifice Ratio = (Old Profit-Sharing Ratio - New Profit-Sharing Ratio) / Old Profit-Sharing Ratio

Substituting the values, we get:

Sacrifice Ratio = ((5x - 3y) : (3x - 2y) : (x - y)) / (5x:3x)

Simplifying the expression, we get:

Sacrifice Ratio = (2x - 3y) : (3x - 2y) : (x - y)

Step 5: Find the Value of x and y

To find the value of x and y, we need to use the given information that the new profit-sharing ratio is 3:2:1.

We can write the new profit-sharing ratio as:

3y:2y:1y = 3:2:1

Equating the corresponding terms, we get:

3y = 3x 2y = 2x 1y = x

Solving these equations, we get:

x = 1 y = 1

Step 6: Calculate the Sacrifice Ratio

Now that we have the values of x and y, we can calculate the sacrifice ratio.

Sacrifice Ratio = (2x - 3y) : (3x - 2y) : (x - y) = (2(1) - 3(1)) : (3(1) - 2(1)) : (1 - 1) = -1 : 1 : 0

Conclusion

In this article, we discussed how to find the sacrifice ratio of old partners when a new partner is admitted into the firm. We used the formula for sacrifice ratio and applied it to an example to illustrate the concept. The sacrifice ratio is an important concept in partnership accounting, as it helps to determine the amount of sacrifice made by the old partners.

Key Takeaways

The sacrifice ratio is the ratio of the difference between the old profit-sharing ratio and the new profit-sharing ratio.
The formula for sacrifice ratio is (Old Profit-Sharing Ratio - New Profit-Sharing Ratio) / Old Profit-Sharing Ratio.
The sacrifice ratio can be calculated using the formula and applying it to an example.
The sacrifice ratio is an important concept in partnership accounting, as it helps to determine the amount of sacrifice made by the old partners.

References

Partnership Accounting, by [Author's Name]
Accounting Standards, by [Author's Name]

Glossary

Sacrifice Ratio: The ratio of the difference between the old profit-sharing ratio and the new profit-sharing ratio.
Old Profit-Sharing Ratio: The profit-sharing ratio of the old partners before the admission of the new partner.
New Profit-Sharing Ratio: The profit-sharing ratio of the old and new partners after the admission of the new partner.
Frequently Asked Questions (FAQs) on Sacrifice Ratio in Partnership Accounting

In our previous article, we discussed the concept of sacrifice ratio in partnership accounting and how to calculate it. However, we understand that there may be many questions and doubts that readers may have regarding this topic. In this article, we will address some of the frequently asked questions (FAQs) on sacrifice ratio in partnership accounting.

Q1: What is the sacrifice ratio in partnership accounting?

A1: The sacrifice ratio is the ratio of the difference between the old profit-sharing ratio and the new profit-sharing ratio. It is calculated by finding the difference between the old and new profit-sharing ratios and then dividing it by the old profit-sharing ratio.

Q2: How is the sacrifice ratio calculated?

A2: The sacrifice ratio is calculated using the formula:

Sacrifice Ratio = (Old Profit-Sharing Ratio - New Profit-Sharing Ratio) / Old Profit-Sharing Ratio

Q3: What is the significance of sacrifice ratio in partnership accounting?

A3: The sacrifice ratio is an important concept in partnership accounting, as it helps to determine the amount of sacrifice made by the old partners when a new partner is admitted into the firm.

Q4: How does the sacrifice ratio affect the old partners?

A4: The sacrifice ratio affects the old partners by reducing their share in the profits and losses of the firm. The old partners have to sacrifice some of their share in the profits and losses to accommodate the new partner.

Q5: Can the sacrifice ratio be negative?

A5: Yes, the sacrifice ratio can be negative. This means that the old partners are gaining from the admission of the new partner, rather than sacrificing.

Q6: How is the sacrifice ratio used in practice?

A6: The sacrifice ratio is used in practice to determine the amount of sacrifice made by the old partners when a new partner is admitted into the firm. It is also used to calculate the amount of goodwill or badwill that the old partners have to pay or receive.

Q7: Can the sacrifice ratio be zero?

A7: Yes, the sacrifice ratio can be zero. This means that the old partners are not sacrificing any of their share in the profits and losses of the firm.

Q8: How does the sacrifice ratio affect the new partner?

A8: The sacrifice ratio affects the new partner by determining the amount of share they will get in the profits and losses of the firm. The new partner will get a share in the profits and losses that is equal to the sacrifice ratio.

Q9: Can the sacrifice ratio be changed?

A9: Yes, the sacrifice ratio can be changed. This can happen if the old partners agree to change the profit-sharing ratio or if the new partner agrees to change the sacrifice ratio.

Q10: What are the implications of sacrifice ratio in partnership accounting?

A10: The sacrifice ratio has significant implications in partnership accounting, as it affects the amount of share that the old and new partners will get in the profits and losses of the firm. It also affects the amount of goodwill or badwill that the old partners have to pay or receive.

Conclusion

In this article, we have addressed some of the frequently asked questions (FAQs) on sacrifice ratio in partnership accounting. We hope that this article has provided readers with a better understanding of the concept of sacrifice ratio and its significance in partnership accounting.

Key Takeaways

The sacrifice ratio is the ratio of the difference between the old profit-sharing ratio and the new profit-sharing ratio.
The sacrifice ratio is calculated using the formula: (Old Profit-Sharing Ratio - New Profit-Sharing Ratio) / Old Profit-Sharing Ratio.
The sacrifice ratio affects the old partners by reducing their share in the profits and losses of the firm.
The sacrifice ratio can be negative, zero, or positive.
The sacrifice ratio has significant implications in partnership accounting, as it affects the amount of share that the old and new partners will get in the profits and losses of the firm.

References

Partnership Accounting, by [Author's Name]
Accounting Standards, by [Author's Name]

Glossary

Sacrifice Ratio: The ratio of the difference between the old profit-sharing ratio and the new profit-sharing ratio.
Old Profit-Sharing Ratio: The profit-sharing ratio of the old partners before the admission of the new partner.
New Profit-Sharing Ratio: The profit-sharing ratio of the old and new partners after the admission of the new partner.