Explanation:

- Initial Profit Sharing Ratio:

- P : Q : R = 4 : 3 : 2.

- Q's Share:

- Q's share is \( \frac{3}{4+3+2} = \frac{3}{9} = \frac{1}{3} \).

- Reallocation of Q's Share:

- Q's share of \( \frac{1}{3} \) is taken by P and R in 3 : 2 ratio.

- P's New Share:

- P takes \( \frac{3}{5} \) of Q's \( \frac{1}{3} \) share = \( \frac{3}{5} \times \frac{1}{3} = \frac{1}{5} \).

- New share of P = original share + additional share = \( \frac{4}{9} + \frac{1}{5} = \frac{20+9}{45} = \frac{29}{45} \).

- R's New Share:

- R takes \( \frac{2}{5} \) of Q's \( \frac{1}{3} \) share = \( \frac{2}{5} \times \frac{1}{3} = \frac{2}{15} \).

- New share of R = original share + additional share = \( \frac{2}{9} + \frac{2}{15} = \frac{10+6}{45} = \frac{16}{45} \).

- New Profit Sharing Ratio:

- P : R = \( \frac{29}{45} : \frac{16}{45} \) = 29 : 16.

- Correct Answer: Option 2 (29 : 16)