Explanation:

Here’s an explanation of each step and the options:

- Initially, A and B share profits in the ratio of 2:1, meaning A has 2/3 and B has 1/3 share.

- C is introduced and gets a 1/4 share in the profits.

- C acquires 3/4 of his 1/4 share from A (which equals 3/16) and 1/4 from B (which equals 1/16).

- After giving 3/16 to C, A's new share is 2/3 - 3/16 = 9/16.

- B's new share after giving 1/16 to C is 1/3 - 1/16 = 4/16.

- C's share is 1/4, or 4/16.

Now, let's analyze the options:

- Option 1: 2 : 1 : 1 does not match the derived ratio.

- Option 2: 23 : 13 : 12 matches perfectly when expressed in a common denominator.

- Option 3: 3 : 1 : 1 does not match the derived ratio.

- Option 4: 13 : 23 : 12 does not match the derived ratio.

The correct answer is:

Option 2: 23 : 13 : 12