Given information:
- Partners in a firm: A, B, C
- Profit sharing ratio before admitting D: 5:3:8
- New profit sharing ratio after admitting D: 3:2:2:3

To find:
- Sacrificing ratio

Solution:
Step 1: Calculate the gaining ratio
The gaining ratio is the ratio in which the new partner (D) acquires the share from the existing partners (A, B, C). It is calculated as follows:

Gaining ratio = New ratio - Old ratio

The old ratio is the profit sharing ratio before admitting D, and the new ratio is the profit sharing ratio after admitting D.

Old ratio of A:B:C = 5:3:8
New ratio of A:B:C:D = 3:2:2:3

Gaining ratio of D from A = 3 - 5 = -2
Gaining ratio of D from B = 2 - 3 = -1
Gaining ratio of D from C = 2 - 8 = -6

Step 2: Calculate the sacrificing ratio
The sacrificing ratio is the ratio in which the existing partners (A, B, C) give up their share to accommodate the new partner (D). It is calculated as follows:

Sacrificing ratio = Gaining ratio / |Gaining ratio|

The sacrificing ratio is always positive.

Sacrificing ratio of A = |(-2)| = 2
Sacrificing ratio of B = |(-1)| = 1
Sacrificing ratio of C = |(-6)| = 6

Therefore, the sacrificing ratio is 2:1:6.

Explanation:
- The profit sharing ratio of the partners in the firm before admitting D was 5:3:8.
- After admitting D, the new profit sharing ratio became 3:2:2:3.
- To calculate the sacrificing ratio, we first calculate the gaining ratio of D from each partner.
- The gaining ratio of D from A is -2, from B is -1, and from C is -6.
- The sacrificing ratio is the absolute value of the gaining ratio.
- Therefore, the sacrificing ratio of A is 2, of B is 1, and of C is 6.
- The sacrificing ratio indicates the proportion in which the existing partners give up their share to accommodate the new partner.