Accountancy, asked by urspari, 1 month ago

12. (NPS in different cases) A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. C joins the firm for a quarter share in the future profits. Ascertain the future profit sharing ratio of partners in each of the following cases : (a) If he acquires his share of profits from the original partners in their profit sharing ratio. (b) If he acquires his share of profits from the partners equally. (c) If he acquires his share of profits from the original partners in the ratio of 2 : 3. [Ans. (a) 9: 6:5 (6) 19:11:10 (c) 10:5:5).

Answers

Answered by Equestriadash

Case (a):

If he acquires his share of profits from the original partners in their profit-sharing ratio.

A's share = 3/5

B's share = 2/5

As mentioned in the question, C is admitted for a quarter of the shares, i.e., 1/4th of the shares.

Let the total profit be assumed to be 1.

The remaining share = 1 - 1/4 = 3/4

The remaining share will be distributed among A and B in their profit-sharing ratio, i.e., 3:2.

A's share:

3/4 × 3/5 = 9/20

B's share:

3/4 × 2/5 = 6/20

C's share:

1/4, or 5/20

Therefore, the new profit-sharing ratio is 9:6:5.

Case (b):

If he acquires his share of profits from the partners equally.

This indicates that C must get shares from A and B in a way that it adds upto 1/4.

Since it has to be obtained from two partners, 1/4 will be divided by 2.

From A, C gets:

1/4 ÷ 2 = 1/4 × 1/2 = 1/8

From B, C gets:

1/4 ÷ 2 = 1/4 × 1/2 = 1/8

Calculation of the new ratio:

New ratio = Old ratio - Ratio surrendered

For A:

New ratio = 3/5 - 1/8 = (24 - 5)/40 = 19/40

For B:

New ratio 2/5 - 1/8 = (16 - 5)/40 = 11/40

For C:

1/4, or 10/40

Therefore, the new profit-sharing ratio is 19:11:10.

Case (c):

If he acquires his share of profits from the original partners in the ratio of 2 : 3.

C must get 1/4 from A and B in the ratio 2:3.