Question

A, B and C are the partners sharing profit in the ratio of 20 %, 40 % and 40 % respectively.
They admitted D as a new partner for 1/15th share in profit. D is to receive his share from
B and C in the ratio of 3:2.​

Answer 1

Given:

• A, B and C are partners sharing profits and losses in the ratio 20%, 40% and 40% respectively, i.e., 1:2:2.
• D is admitted as a new partner for 1/15th of share profits/losses.
• D acquires his share from B and C in the ratio 3:2.

To find: The new profit-sharing ratio.

Answer:

• A's old share = 1/5
• B's old share = 2/5
• C's old share = 2/5
• D's share = 1/15

Since D gets his share from B and C in the ratio of 3:2, 1/15 will need to be divided in the ratio 3:2 to obtain how much B and C will be sacrificing.

From B, D gets:

• 1/15 × 3/5 = 3/75

From C, D gets:

• 1/15 × 2/5 = 2/75

Calculation of the new profit sharing ratio:

New ratio = Old ratio - Sacrifice made

For A:

• New ratio = 1/5 - 0 = 1/5, or 15/75 [A made no sacrifice for D and hence there is no change.]

For B:

• New ratio = 2/5 - 3/75 = (30 - 3)/75 = 27/75

For C:

• New ratio = 2/5 - 2/75 = (30 - 2)/75 = 28/75

For D:

• New ratio = 1/15, or 5/75

Therefore, the new profit-sharing ratio is 15:27:28:5.