Explanation:

- Initially, A and B share profits in the ratio of 2:3. This means A's share is 2/5 and B's share is 3/5.

- C is admitted with a 1/5 share, which is taken entirely from A's share.

- After giving 1/5 from A's share to C, A’s new share is 2/5 - 1/5 = 1/5.

- The new profit-sharing ratio will have A with 1/5, B with 3/5, and C with 1/5.

- To convert their shares into a common denominator, we have A as 1/5, B as 3/5, and C as 1/5. This translates to a ratio of 1:3:1.

Therefore, the correct new profit-sharing ratio is:

- Option 4: 1 : 3 : 1

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