Explanation:

Let's break down the problem step by step:

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

- C is admitted with a 1/4th share. This means A and B now share 3/4th of the profits.

- The portion for C is 1/4th of the total profit.

- The original 3:2 ratio between A and B now applies to their 3/4th share.

- A's new share: \( \frac{3}{5} \times \frac{3}{4} = \frac{9}{20} \)

- B's new share: \( \frac{2}{5} \times \frac{3}{4} = \frac{6}{20} \)

- C's share is already set at \( \frac{5}{20} \).

Now, D enters for 20 paisa in the rupee, which equals a 1/5th = 20% share of the profits. The rest 80% of the profits are divided among A, B, and C.

To find the new ratio:

- A's share: \( \frac{9}{20} \times \frac{4}{5} = \frac{36}{100} \)

- B's share: \( \frac{6}{20} \times \frac{4}{5} = \frac{24}{100} \)

- C's share: \( \frac{5}{20} \times \frac{4}{5} = \frac{20}{100} \)

- D's share (new admission): \( \frac{20}{100} \)

Converting these into whole numbers, divide each part by 4:

- A: 9

- B: 6

- C: 5

- D: 5

The new profit sharing ratio is 9 : 6 : 5 : 5.

- Option 1 (9 : 6 : 5 : 5) matches this calculation.