Explanation:

- A, B, C, and D initially share profits in the ratio of 9:6:5:5.

- This adds up to a total of 25 parts.

- E joins for a 20% share, which means the existing partners share 80% of the profits.

- The new sharing among A, B, C, and D is provided as fractions: 3/10, 4/10, 2/10, 1/10.

- These fractions together add up to 1, ensuring that A, B, C, and D share 80% of the remaining profit (0.8 of profit).

- Total present ratio between A, B, C, and D = 3+4+2+1 = 10 parts.

- Adjusting 80% for A, B, C, and D gives: 3/10, 4/10, 2/10, 1/10 converted to 3/10*8, 4/10*8, 2/10*8, 1/10*8 and rounded to whole numbers = 6:8:4:2.

- Adding E’s share: 6:8:4:2:5.

Answer: 6:8:4:2:5