There is change in the profit sharing ratio of the existing partners also, depending on the partnership agreement. There can be following cases in this regard:

Case I

When new partner’s share is given but the question is silent about the share/sacrifice/surrendered share of the old partners then it is assumed that the old partners will share the remaining share in their old profit sharing ratio.

Example:

A and B are partners sharing profits in the ratio 3:2. They admit C for 1/3 share in future profits.

Total profit = 1

C’s Share = 1/3

Remaining Profit = 1 – 1/3 = 2/3

This remaining share of 2/3 will be shared between A and B in the ratio 3:2

So A’s share = 2/3 × 3/5 = 6/15

B’s share = 2/3 × 2/5 = 4/15

C’s share = 1/3 × 5/5 = 5/15

New ratio = 6/15: 4/15: 5/15 = 6:4:5

[Denominators must be made equal while calculating the ratio and new ratio must be written in the same sequence, taking the new partner in the end. To check, the total of the numerators should be equal to the denominator. ]

Case II

When new partner purchases/gets/acquires/takes  his share from old partners in a particular ratio then the new ratio of the old partners will be calculated by subtracting the proportion given to the new partner from the shares of old partners .

Example:

A and B are partners sharing profits in the ratio 3:2. They admit C as new partners for 1/3 share in future profits which he gets 1/9 from A and 2/9 from B.

A’s old share = 3/5[‘C gets’ means, A gives/ sacrifices in favor of C i.e. 1/9]

So, A’s new share = 3/5 – 1/9 = 22/45

B’s old share = 2/5[‘C gets’ means, B gives/ sacrifices in favor of C i.e. 2/9]

So, B’s new share = 2/5 – 2/9 = 8/45

C’s new share = 1/9 x 5/5 = 5/45

New ratio = 22: 8: 5

Case III

When the old partners surrender/give/sacrifice a particular fraction/share of their share in favor of new partner.

Example:

A and B are partners sharing profits in the ratio 3:2. They admit C as a new partner for whom A surrenders 1/3rd of his share and B surrenders 2/3rd of his share .

A’s old share = 3/5 and A surrenders/sacrifices/gives in favor of C = 3/5 x 1/3 = 3/15

A’s new share = 3/5 – 3/15 = 6/15

B’s old share = 2/5 and B surrenders/sacrifices/gives in favor of C = 2/5 x 2/3 = 4/15

B’s new share = 2/5 – 4/15 = 2/15

C’s share = 3/15 + 4/15 = 7/15[share taken from A and B combined]

New ratio = 6:2:7

Case IV

When a new partner acquires/takes/purchases his share entirely/wholly from the new partner.

Example:

A and B are partners sharing profits in the ratio 3:2. They admit C for 1/5th share in profits which he acquires entirely from A.

A’s old share = 3/5 and A sacrifices in favor of C = 1/5

A’s new share = 3/5 – 1/5 = 2/5

B’s share = 2/5[remaining as before]

C’s share = 1/5[taken from A]

New ratio = 2:2:1

Case V

When a new partner acquires/purchases/takes/gets his share from the old partners in a certain ratio.

Example:

A and B are partners sharing profits in the ratio 3:2. C is admitted for 1/3rd share which he acquires from A and B in the ratio of 2:1.

A’s old share = 3/5, [C acquires means A’s sacrifice] = 2/3 × 1/3 = 2/9

A’s new share = 3/5 – 2/9 =17/45

B’s old share = 2/5, [C acquires means B’s sacrifice = 1/3× 1/3 = 1/9

B’s new share = 2/5 – 1/9 = 13/45

C’s share = 1/3 ×15/15 =15/45

New ratio = 17:13:15

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