In case there is no information regarding the acquisition of a share in profit of the retiring/deceased partner by the remaining partners, the assumption is that they will acquire his/her share in the:

When a partner retires or dies and there is no specific information about how the remaining partners will acquire the outgoing partner's share, two concepts apply simultaneously:

Acquisition in Old Profit Sharing Ratio

The remaining partners acquire the retiring/deceased partner's share in the ratio of their existing (old) shares among themselves.

For example, if partners A, B, and C share profits in 5:3:2 and C retires:

• A and B will acquire C's share in the ratio of 5:3 (their old ratio among themselves)
• If C's share is 2/10, then A gains 5/8 of 2/10 and B gains 3/8 of 2/10

Gaining Ratio

The gaining ratio is calculated as: $\text{New Ratio} - \text{Old Ratio}$

This ratio represents what each remaining partner gains from the retiring partner's share. When partners acquire in their old profit sharing ratio, this automatically creates the gaining ratio.

Using the same example:

• A's new share = 5/10 + (5/8 × 2/10) = 31/50
• B's new share = 3/10 + (3/8 × 2/10) = 19/50
• Gaining ratio of A:B = (31/50 - 5/10) : (19/50 - 3/10) = 5:3

Both options describe the same outcome - Option 1 explains the method of acquisition (in old ratio among themselves), while Option 4 represents the resulting ratio that emerges from this distribution. Hence, both are correct.