The correct answer is $\boxed{\text{B. 28 : 21 : 14 : 9}}$.
The initial profit sharing ratio of A, B, and C is 4 : 3 : 2. The total number of parts is $4 + 3 + 2 = 9$. When D is added to the partnership, the new total number of parts is $9 + 1 = 10$. To get the new profit sharing ratio, we multiply each partner’s original share by the new total number of parts divided by the original total number of parts. So, A’s new share is $4 \times \frac{10}{9} = \frac{40}{9}$, B’s new share is $3 \times \frac{10}{9} = \frac{30}{9}$, C’s new share is $2 \times \frac{10}{9} = \frac{20}{9}$, and D’s new share is $\frac{1}{8} \times \frac{10}{9} = \frac{5}{72}$. Therefore, the new profit sharing ratio is $\frac{40}{9} : \frac{30}{9} : \frac{20}{9} : \frac{5}{72} = 28 : 21 : 14 : 9$.
Option A is incorrect because it does not take into account the fact that D is being given a $\frac{1}{8}$ share. Option C is incorrect because it does not take into account the fact that the total number of parts is now 10. Option D is incorrect because it does not take into account the fact that A, B, and C are sharing profits and losses in the ratio of 4 : 3 : 2.