At the time of admission of the new partner into the firm there is a need to calculate tne new profit sharing ratio of the firm.

There are different cases for the calculation of new ratio:

Case 1. When only the share of new partner is given in the question

In this case it is assumed that the old partners will continue to share the remaining profits in the same ratio in which they were sharing before the admission of the new partner.

Illustration 1. A and B are partners in the ratio 2:3. They admitted C into the partnership with 1/4th share.Calculate the new profit sharing ratio of the firm.

Solution

Let total profits = 1

Share = 1/4

Remaining share = 1 – 1/4 = 3/4

A’s share = 2/5 of 3/4 = 6/20

B’s share = 3/5 of 3/4 = 9/20

C’s share = 1/4 = 5/20

Thus the new ratio among A,B and C is 6/20 : 9/20 : 5/20 i.e. 6:9:5.

Case 2. When the new partner purchases his share form the old partners

In this case we deduct the share given to the new partner by the old partners to get their new share and calculate thier new ratio.

Illustration 2. X and Y are partners in the ratio 2:1. They admit Z into the firm with 3/7 th share which he gets 2/7 from X and 1/7 from Y. Calculate the new profit sharing ratio.

Solution

X’s old share = 2/3

X’s sacrifice for Z = 2/7

X’s new share = 2/3 − 2/7 = 8/21

Y’s old share = 1/3

Y’s sacrifice for Z = 1/7

Y’s new share=1/3 − 1/7 = 4/21

Z’s share = 3/7 = 2/7 + 1/7 = 3/7 = 9/21

New Profit sharing Ratio among X, Y and Z is 8:4:9

Case 3. When old partners surrender a particular fraction of their share in favour of new partner:

In this case first calculate the share surrendered by old partners in favour of new partner. From the old share of old partners, subtract their surrendered share to get their new share. Now add share surrendered by old partners to get the share of new partner.

Illustration 3. X and Y are Partners sharing profits and losses in the ratio 2:1. They admit Z into the firm. X surrenders 1/4th of his share and Y surrenders 3/4th of his share in favour of Z. Calculate their new profit sharing ratio.

Solution:

X’s old share= 2/3

Share surrendered in favour of Z = 2/3 × 1/4 = 1/6

X’s new share = 2/3 − 1/6 = 3/6

Y’s old share= 1/3 Share surrendered in favour of Z = 1/3×3/4 = 1/4

Y’s new share = 1/3? 1/4 = 1/12

Z’s share = 1/6 + 1/4 = 5/12

New Profit Sharing Ratio among X, Y and Z is 3/6 : 1/12 : 5/12 i.e. 6 : 1: 5