Explanation:

- Old Profit Sharing Ratio:

- P, Q, and R share profits in the ratio 2:2:1.

- This implies P has 2/5, Q has 2/5, and R has 1/5 of the profits.

- When Q Retires:

- Q's share (2/5) will be taken over by P and R in a new ratio.

- New Profit Sharing Ratio:

- P and R have a new ratio of 3:1.

- Total parts = 3 + 1 = 4

- P gets 3/4 and R gets 1/4 of the remaining profits.

- Calculation of Gaining Ratio:

- P's new share of total profit = 3/4

- R's new share of total profit = 1/4

- P was originally getting 2/5.

- R was originally getting 1/5.

- Gaining for P = (3/4 - 2/5) = 7/20

- Gaining for R = (1/4 - 1/5) = 1/20

- Gaining ratio of P:R = 7:1 Correct Answer