Question

A and B are partners sharing profits and losses in the ratio of 5 : 3. They admit C into partnership giving him 1/4 share in profits which he acquires from A and B in the ratio of 3 : 1. Calculate the new profit sharing ratio.

Answer 1

Given old ratio A : B = 5 : 3.

Total parts = 8.

So:

A's old share = `5/8`

B's old share = `3/8`

C gets `1/4` share, which he acquires from A and B in the ratio 3 : 1.

Step 1: C's share acquired from A

`1/4 xx 3/4 = 3/16`

Step 2: C's share acquired from B

`1/4 xx 1/4 = 1/16`

Step 3: Calculate new shares

A: `5/8 - 3/16 = (10 - 3)/16 = 7/16`

B: `3/8 - 1/16 = (6 - 1)/16 = 5/16`

C: `1/4 = 4/16`

Therefore:

A : B : C = `7/16 : 5/16 : 4/16`

A : B : C = 7 : 5 : 4