# New Profit Sharing and Gaining Ratio: Calculations with Solved Examples

The compilation of these Retirement or Death of a Partner Notes makes students exam preparation simpler and organised.

## New Profit Sharing and Gaining Ratio

On the death or retirement of a partner, the partnership firm will be reconstituted. One major change will be the change in the profit-sharing ratios of the remaining partners. Let us see how the gaining ratio and sacrificing ratio will be calculated.

### New Profit Sharing Ratio

There are different cases when a partnership can have a new profit sharing ratio:

• Sometimes the partners may decide to change their existing profit sharing ratio, without any admission or retirement of a partner.
• At the time of admission of the new partner.
• At the time of retirement or death of an old partner.

This may result in again to a few partners and loss to others. The partners who are in profit due to this change in the profit-sharing ratio should compensate the sacrificing partner/partners.

New profit sharing ratio: Ratio in which the partners decide to share profits/losses in the future.

Gaining ratio: Ratio in which the partners have agreed to gain their share of profit from other partners.

Sacrificing ratio: Ratio in which the partners have agreed to sacrifice their share of profit in favour of other partners.
Sacrificing ratio = Old Ratio – New Ratio

### Gaining Ratio

The gaining ratio is calculated at the time of retirement or the death of a partner. It is the ratio in which the remaining partners acquire the outgoing partner’s share of profit.

When the partner retires, the profit-sharing ratio of the continuing partners gets changed. Continuing partners distribute the share of retiring partners among them.

Gaining ratio = New Ratio – Old Ratio (if positive)

Examples:

Question:
Various cases of new ratio and gaining ratio are explained as follows:

Case 1: When the share of retiring partner is acquired by old partners in an old ratio
Amit, Sumit, and Punit share profit and losses in the ratio of 3 : 2 : 1, respectively. Amit retires and the remaining partners decide to share to take Amit’s share in the existing ratio i.e. 2 : 1. Calculate the new ratio and gaining ratio.
Solution:
The existing ratio between Sumit and Punit = 2/6 and 1/6
Amit’s ratio (retiring partner) = 3/6
Amit’s share taken by Sumit and Punit in the ratio of 2 : 1
Sumit gets = 3/6 × 2/3 = 6/18
Punit gets = 3/6 × 1/3 = 3/18
New ratio between Sumit and Punit is = 6 : 3 = 2 : 1
Gaining ratio = New Ratio – Old Ratio
Sumit’s gain = 2/3 – 2/6 = 2/6
Punit’s gain = 1/3 – 1/6 = 1/6
Gaining ratio = 2 : 1
New Ratio = 2 : 1

Case 2: When the share of retiring partner is acquired by old partners in old specified proportions
Amit, Sumit, and Punit share profit and losses in the ratio of 2 : 3 : 1, respectively. Amit retires and the remaining partners decide to share to take Amit’s share equally. Calculate the new ratio and gaining ratio.
Solution:
The existing ratio between Sumit and Punit = 3/6 and 1/6
Amit’s ratio (retiring partner) = 2/6
Amit’s share taken by Sumit and Punit in the ratio of 1 : 1
Sumit gets = 2/6 × 1/2 = 1/6
Sumit’s new share = 3/6 + 1/6 = 4/6
Punit gets = 2/6 × 1/2 = 1/6
Punit’s new share = 1/6 + 1/6 = 2/6
New ratio between Sumit and Punit is = 4 : 2 = 2 : 1
Gaining ratio is given the question i.e. 1 : 1
Gaining ratio = 1 : 1
New Ratio = 2 : 1

Case 3: When the share of the retiring partner is acquired fully by one of the continuing partners
Amit, Sumit, and Punit share profit and losses in the ratio of 4 : 5 : 2, respectively. Amit retires and Punit acquires Amit’s share. Calculate the new ratio and gaining ratio.
Solution:
Punit’s new share = 2/11 + 4/11 = 6/11
Sumit share remains unchanged = 5/11
The new ratio between Sumit and Punit is = 5 : 6
The gaining ratio in this case between Sumit and Punit will be
Sumit’s gain = 5/11 – 5/11 = Nil
Punit’s gain = 6/11 – 2/11 = 4/11
This shows that the entire gain is taken by Punit.