Explanation:

- Original Profit Sharing: P, Q, and R share profits in the ratio of 5:4:3.

- Q Retires: With Q leaving, only P and R remain as partners.

- New Profit Ratio: P and R decide to share profits equally, which is a ratio of 1:1.

- Old Share vs. New Share:

- P's old share was 5/12.  P's new share is 1/2 (or 6/12).

- R's old share was 3/12.  R's new share is 1/2 (or 6/12).

- Gaining Ratio 

- P gains: 6/12 - 5/12 = 1/12.

- R gains: 6/12 - 3/12 = 3/12.

- Gaining Ratio: P:R = 1:3.

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