**Sacrificing and Gaining Ratio**

In a partnership, the sacrificing ratio refers to the ratio in which the partners agree to give up their current profit sharing ratio. On the other hand, the gaining ratio refers to the ratio in which the partners agree to gain from the sacrificed ratio. Let's understand this concept with the help of two scenarios:

**Scenario 1: 3:2:1**

Assume that there are three partners in a business with a profit sharing ratio of 3:2:1. Now, if the partners decide to change their profit sharing ratio, they need to determine the sacrificing and gaining ratio.

Let's say the new profit sharing ratio is 1:1:1. To calculate the sacrificing ratio, we subtract the new ratio from the old ratio:

Sacrificing ratio of Partner A = (Old ratio - New ratio) = (3 - 1) = 2
Sacrificing ratio of Partner B = (2 - 1) = 1
Sacrificing ratio of Partner C = (1 - 1) = 0

Hence, the sacrificing ratio is 2:1:0.

To calculate the gaining ratio, we subtract the sacrificing ratio from the new ratio:

Gaining ratio of Partner A = (New ratio - Sacrificing ratio) = (1 - 2) = -1
Gaining ratio of Partner B = (1 - 1) = 0
Gaining ratio of Partner C = (1 - 0) = 1

Hence, the gaining ratio is -1:0:1.

**Scenario 2: 1:1:1**

Now, let's consider another scenario where the original profit sharing ratio is 1:1:1, and the partners decide to change it to a new ratio of 3:2:1.

Sacrificing ratio of Partner A = (Old ratio - New ratio) = (1 - 3) = -2
Sacrificing ratio of Partner B = (1 - 2) = -1
Sacrificing ratio of Partner C = (1 - 1) = 0

Hence, the sacrificing ratio is -2:-1:0.

Gaining ratio of Partner A = (New ratio - Sacrificing ratio) = (3 - (-2)) = 5
Gaining ratio of Partner B = (2 - (-1)) = 3
Gaining ratio of Partner C = (1 - 0) = 1

Hence, the gaining ratio is 5:3:1.

**Change in Profit Sharing Ratio**

When there is a change in the profit sharing ratio, it implies that partners are agreeing to distribute profits and losses in a different proportion. This change can occur due to various reasons such as changes in capital contribution, changes in responsibilities, or changes in the partnership agreement.

The change in profit sharing ratio affects the distribution of profits and losses among partners. The partner with a higher gaining ratio will receive a larger share of profits, while the partner with a higher sacrificing ratio will receive a lesser share.

It is important to note that a change in the profit sharing ratio does not necessarily mean a change in the partnership itself. The partnership continues to exist, but the distribution of profits and losses is altered based on the new ratio agreed upon by the partners.

In conclusion, the sacrificing and gaining ratio