At the time of the admission of a new partner, there is a change in the profit sharing ratio of the old partners also. The new profit sharing ratio is calculated after considering the new partner’s share in profit and the sacrifice made by the old partners. Here, we will discuss various cases to calculate the new profit sharing ratio.

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**New Profit Sharing Ratio**

New profit sharing ratio is the ratio in which all the partners, including new or incoming partner, will share future profits and losses of the firm.

**Browse more Topics under Admission Of A New Partner**

**Computation of New Profit Sharing Ratio**

In this case, we will assume that old partners will make the sacrifice in their old profit sharing ratio. Therefore, sacrificing ratio will always be the old profit sharing ratio.

Of course, the new profit sharing ratio will be different but there will be no change in profit sharing ratio of the old partners. (see solved example 1)

In this case, new partners will purchase his share from old partners in a particular ratio. So we will deduct the amount that the new partner will purchase old partners in their particular ratio and then we will calculate the new profit sharing ratio of all the partners.

*Learn more about Gaining Ratio here in detail.*

In this case, we will deduct the share surrender from each old partner to determine his share in the reconstituted firm.

The share that old partners will surrender in favour of the new partner will be added. It will be the share of the new partner.

In this case, the new partner will acquire his entire share from one partner. We will calculate the sacrificing share of that partner and hat share will be deducted from his ratio and the deducted ratio will be added to the new partner.

That will be his profit sharing ratio. There will be no change in profit sharing ratio of other partners as they are not sacrificing any share.

The new partner may acquire a part of the share of profits from one partner and balance part of the profit from another partner.

In such a case, old partners share of profit will change to the extent of share sacrificed by them. We will deduct the share sacrificed by old partners and will add to the new partner.

**Sacrificing Ratio**

Sacrificing ratio is the ratio in which old or existing partners forego, i.e., sacrifice their share of profit in favour of the new or incoming partner.

This share may be given (sacrificed) to the new partner by all the old partners equally or by all or some of the partners in an agreed ratio.

**Sacrificing Ratio = Old Ratio – New Ratio**

**Sacrificing Partner**

The partner whose share decreases by the change in profit sharing ratio is sacrificing partner.

**Gaining Ratio**

It is the ratio in which partners have agreed to gain their shares in profit from other partners of the firm.

**Gaining Ratio = New Ratio – Old Ratio**

**Gaining Partner**

The partner whose share increases by the change in profit sharing is the gaining partner.

**Solved Example on New Profit Sharing Ratio**

**Q. Find a new profit sharing ratio for the following:**

- A and B are partners sharing profits in the ratio of 3:1. C is admitted for the 1/8
^{th}share of the profits. - X and Y are partners sharing profits and losses in the ratio of 7:5. They admit Z, a new partner, who acquires 1/12
^{th}from X and 1/6^{th}from Y as his share. - A and B are partners in the firm sharing profits and losses in the ratio of 5:3. A surrenders 1/20
^{th}of his share, whereas B surrenders 1/24^{th}of his share in favour of C, a new partner. - N and M are partners sharing profits in the ratio of 2:1. They admit O into the partnership for the 1/4
^{th}share of profit. O has acquired the share from old partners in the ratio of 3:2. - P and Q are partners sharing profit and losses in the ratio of 5:3. R is admitted for 1/5
^{th}share and he acquires all his share from P.

**Ans:**

- Since C’s share is given without mentioning as to what C acquires from A and B separately, C acquires his share from A and B in their old profit sharing ratio. Therefore, sacrificing ratio by A and B will be 3:1.

Firm’s share = 1

Remaining share = 1- \(\frac{1}{8}\)

= \(\frac{7}{8}\)

Now,

A’s new share = \(\frac{3}{4}\) x \(\frac{7}{8}\) = \(\frac{21}{32}\)

B’s new share = \(\frac{1}{4}\) x \(\frac{7}{8}\) = \(\frac{7}{32}\)

C’s share = \(\frac{1}{8}\) x \(\frac{7}{8}\) = \(\frac{4}{32}\)

New profit sharing ratio of A : B : C = 21 : 7 : 4

- Old profit sharing ratio of X and Y = 7:5

Z acquires \(\frac{1}{12}\)^{th} from X and \(\frac{1}{6}\)^{th} from Y

Z’s total share = \(\frac{1}{12}\) + \(\frac{1}{6}\) = \(\frac{3}{12}\)

X’s new share = \(\frac{7}{12}\) – \(\frac{1}{12}\) = \(\frac{6}{12}\)

Y’s new share = \(\frac{5}{12}\) – \(\frac{1}{6}\) = \(\frac{3}{12}\)

Hence, new profit sharing ratio of X : Y : Z = 6 : 3 : 3 or 2 : 1 : 1

- A’s share = \(\frac{5}{8}\)

A surrenders in favour of C = \(\frac{1}{20}\) x \(\frac{5}{8}\) = \(\frac{1}{32}\)

So, A’s new share = \(\frac{5}{8}\) – \(\frac{1}{32}\) = \(\frac{19}{32}\)

B’s share = \(\frac{3}{8}\)

B surrenders in favour of C = \(\frac{1}{24}\) x \(\frac{3}{8}\) = \(\frac{1}{64}\)

So, Bs new share = \(\frac{3}{8}\) – \(\frac{1}{64}\) = \(\frac{23}{64}\)

Now C will get = \(\frac{1}{32}\) + \(\frac{1}{64}\) = \(\frac{3}{64}\)

New profit sharing ratio of A : B : C = \(\frac{19}{32}\) : \(\frac{23}{64}\) : \(\frac{3}{64}\)

= 38 : 23 : 3

- Calculation of O’s share:

From M = \(\frac{3}{5}\)^{th} of \(\frac{1}{4}\) = \(\frac{3}{20}\) and;

from N = \(\frac{2}{5}\)^{th} of \(\frac{1}{4}\) = \(\frac{2}{20}\)

Now O’s share = \(\frac{3}{20}\) + \(\frac{2}{20}\) = \(\frac{5}{20}\)

As we know,

New share = Old Share – New Share

Therefore , new share of M = \(\frac{2}{3}\) – \(\frac{3}{20}\) = \(\frac{31}{60}\)

And, new share of N = \(\frac{1}{3}\) – \(\frac{2}{20}\) = \(\frac{14}{60}\)

Share of O = \(\frac{1}{4}\) or \(\frac{15}{60}\)

Thus, New Profit Sharing Ratio of M : N : O = \(\frac{31}{60}\) : \(\frac{14}{60}\) : \(\frac{15}{60}\)

= 31 : 14 : 15

- P’s new share = \(\frac{5}{8}\) – \(\frac{1}{5}\)

= \(\frac{17}{40}\)

Q’s share = \(\frac{3}{8}\) or

\(\frac{15}{40}\)

R’s share = \(\frac{1}{5}\) or \(\frac{8}{40}\)

Thus, New Profit Sharing Ratio of P : Q : R = \(\frac{20}{40}\) : \(\frac{12}{40}\) : \(\frac{8}{40}\)

= 5 : 3 : 2