(a)if A retires new ratio between B&C will be 4:1
(b)if B retires new ratio between A&C will be 5:1
(c)if C retires new ratio between A&B will be 5:4

A. A retires:
When A retires, the profit sharing ratio among the remaining partners (B and C) will be recalculated. However, before determining the new ratio, we need to consider the following:

1. Settlement of A's Capital: A's capital account needs to be settled. The amount invested by A will be paid back to him, along with any interest or interest on drawings, if applicable. After deducting this amount from the total capital, the remaining capital will be divided among B and C.

2. Goodwill Adjustment: If there is any change in the profit sharing ratio, goodwill needs to be adjusted. Goodwill is an intangible asset that represents the reputation and customer base of a business. If the retiring partner's share is bought by the remaining partners at a premium, the retiring partner is entitled to a share of the premium. Conversely, if the retiring partner's share is bought at a discount, the remaining partners are entitled to a share of the discount.

Once these adjustments are made, the new profit sharing ratio can be calculated.

B. B retires:
When B retires, the profit sharing ratio among the remaining partners (A and C) will be recalculated. Similar to the case when A retires, we need to consider the following:

1. Settlement of B's Capital: B's capital account needs to be settled. The amount invested by B will be paid back to him, along with any interest or interest on drawings, if applicable. After deducting this amount from the total capital, the remaining capital will be divided among A and C.

2. Goodwill Adjustment: If there is any change in the profit sharing ratio, goodwill needs to be adjusted. The calculations for goodwill adjustment will be the same as in the case of A's retirement.

Once these adjustments are made, the new profit sharing ratio can be calculated.

C. C retires:
When C retires, the profit sharing ratio among the remaining partners (A and B) will be recalculated. Similar to the previous cases, we need to consider the following:

1. Settlement of C's Capital: C's capital account needs to be settled. The amount invested by C will be paid back to him, along with any interest or interest on drawings, if applicable. After deducting this amount from the total capital, the remaining capital will be divided among A and B.

2. Goodwill Adjustment: If there is any change in the profit sharing ratio, goodwill needs to be adjusted. The calculations for goodwill adjustment will be the same as in the previous cases.

Once these adjustments are made, the new profit sharing ratio can be calculated.

To determine the new profit sharing ratio, the remaining partners need to agree on a mutually beneficial ratio that reflects their respective contributions, efforts, and expectations. This ratio should be fair and in line with the partnership agreement or any new terms negotiated among the partners.