Explanation:

- Initially, L, P, and G share profits in the ratio of 15 : 9 : 8, respectively.

- Upon G's retirement, L and P decide to equally share profits, which becomes a 1:1 ratio between them.

- To find the gaining ratio, subtract the old ratio from the new ratio for each partner.

- L's position: Old share = 15/32, New share = 1/2 = 16/32, Difference = 16/32 - 15/32 = 1/32.

- P's position: Old share = 9/32, New share = 1/2 = 16/32, Difference = 16/32 - 9/32 = 7/32.

- Therefore, the gaining ratio is 1:7.

- Option:1, 15 : 9, is incorrect; this is the old ratio of L and P.

- Option:2, 9 : 15, is not relevant; it doesn't reflect the new or gaining ratio.

- Option:3, 7 : 1, is incorrect based on the calculations.

- Option:4, 1 : 7, is correct and matches the gaining ratio.