Question

A and B share profits and losses in the ratio of 3/2 They admit C as a new partner for 1/3 share in the profits of the firm which he acquired from A and B in the ratio of 2:3 After some time, they admitted D as a new partner for 1/5 share profits which he acquired equally from A and C. Calculate: (1) New profit sharing ratio of A, B and C;
(ii) New profit sharing ratio of A, B , C and D​

Answer 1

Given:

• A and B are partners in a firm, sharing profits and losses in the ratio 3:2.
• C is admitted into the firm for 1/3rd share, which he acquires from A and B in the ratio 3:2.
• D was later on admitted into the firm as well, for 1/5th share, which he acquires equally from A and C.

To find: The new profit-sharing ratios in both cases.

Answer:

Case 1:

• A's old share = 3/5
• B's old share = 2/5

• C's share = 1/3

C acquires his share, i.e., 1/3, from A and B in the ratio 2:3.

From A, C gets:

• 2/5 × 1/3 = 2/15

From B, C gets:

• 3/5 × 1/3 = 3/15

Calculation of the new profit-sharing ratio:

New share = Old share - Sacrifice made

For A:

• New share = 3/5 - 2/15 = (9 - 2)/15 = 7/15

For B:

• New share = 2/5 - 3/15 = (6 - 3)/15 = 3/15

For C:

• New share = 1/3, or 5/15

Therefore, the new profit-sharing ratio of A, B and C is 7:3:5.

Case 2:

• A's old share = 7/15
• B's old share = 3/15
• C's old share = 5/15

• D's share = 1/5

D acquires his share, i.e., 1/5, from A and C equally.

From A, D gets:

• 1/2 × 1/5 = 1/10

From C, D gets:

• 1/2 × 1/5 = 1/10

There will be no effect on B's share, since he makes no sacrifice for the new partner.

Calculation of the new profit-sharing ratio:

New share = Old share - Sacrifice made

For A:

• New share = 7/15 - 1/10 = (70 - 15)/150 = 55/150

For B:

• New share = 3/15 or 30/150 [no change]

For C:

• New share = 5/15 - 1/10 = (50 - 15)/150 = 35/150

For D:

• New share = 1/5, or 30/150

Therefore, the new profit-sharing ratio of A, B, C and D is 55:30:35:30 or 11:6:7:6.

Answer 2

Solved! Refer to the attachments.