# Calculation of New Profit Sharing Ratio

As soon as a partner retires, the profit sharing ratio of the continuing partners gets changed. The share of the retiring partner is distributed amongst the continuing partners. In the absence of information, the continuing partners take the retiring partnerâ€™s share in their profit sharing ratio. The ratio, in which the continuing partners acquired the share of retiring partner, is called as gaining ratio.

**Note:** When the ratio among the continuing partners remains unchanged, the gaining ratio will be equal to the new ratio.

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

**When retiring partnerâ€™s share acquired by continuing partners in old ratio:** When the continuing partners acquires the retiring partnerâ€™s share in old ratio.

**Illustration - 1**

X, Y and Z are partners sharing profits and losses in the ratio of 4: 3: 2. X retires and the remaining partners decide to take Xâ€™s share in the existing ratio i.e. 3 : 2. Calculate the new ratio of Y and Z.

**Solution:**

Existing ratio between Y and Z = 3/9 and 2/9

Xâ€™s ratio (retiring partner) = 4/9

Xâ€™s share taken by Y and Z in the ratio of 3 : 2

Y gets = 4/9 Ã— 3/5 = 12/45

Yâ€™s new share = 3/9 + 12/45 = 27/45

Z gets = 4/9 Ã— 2/5 = 8/45

Zâ€™s new share = 2/9 + 8/45 = 18/45

New ratio between Y and Z is 27/45:18/45 = 27:18 = 3 : 2

Gaining ratio = New ratio â€“ Existing ratio

Yâ€™s gain = 27/45 â€“ 3/9 = 12/45

Zâ€™s gain = 18/45 â€“ 2/9 = 8/45

12/45 : 8/45 i.e. 3:2

**Gain ratio 3 : 2**

**New ratio 3 : 2**

You may note that the new ratio is similar to the ratio that existed between Y and Z before Xâ€™s retirement.

**Note:** In the absence of any information in the question, it will be presumed that the retiring partnerâ€™s share has been distributed in the old ratio.

**Retiring partnerâ€™s share distributed in specified proportions:** Sometimes, the continuing partners share the retiring partnerâ€™s share in a specified ratio. The share gained by continuing partners is added to their old share to arrive at new share.

**Illustration - 2**

X, Y and Z are partners in a firm, sharing profits in the ratio of 3 : 2 : 1. Y retired and his share was divided equally between X and Z. Calculate the new profit sharing ratio of X and Z.

**Solution:**

Yâ€™s share = 2/6

Yâ€™s share is divided between X and Z in the ratio of 1 : 1

X gets 1/2 of 2/6 = 2/6 Ã— 1/2 = 1/6

Xâ€™s new share = 3/6 + 1/6 = 4/6

Z gets 1/2 of 2/6 = 2/6 Ã— 1/2 = 1/6

Zâ€™s new share = 1/6+1/6 = 2/6

**New ratio 4:2 or 2:1**

**Gain ratio 1:1** (given in the question)

**Retiring partnerâ€™s share taken over by one of the partners:** The retiring partnerâ€™s share may be acquired by one of the continuing partners. In this case, the retiring partnerâ€™s share is added to that of the continuing partnerâ€™s existing share. Only his/her share changes. The other partners continue to share profits in the existing ratio.

**Illustration - 3**

X, Y and Z share profit in the ratio of 5 : 4 : 2. Y retires and his share is acquired by Z.

**Solution:**

So Zâ€™s share is 2/11 + 4/11 = 6/11, Xâ€™s share will remain unchanged i.e., 5/11. Thus, the new profit sharing ratio of X and Z is 5 : 6. Gaining ratio in this case between X and Z will be

Xâ€™s gain 5/11-5/11 = Nil

Zâ€™s gain 6/11-2/11 = 4/11.

This indicates that the entire gain is taken by Z.