Final answer:
The correct answer is option (b) New ratio: 7:3, Gaining ratio: 7:5. The correct response is the new profit-sharing ratio becomes 7:3 since B's departure leaves only A and C, and their gaining ratio is 7:5.
Step-by-step explanation:
When B leaves the partnership, only A and C remain to share the profits. The new profit-sharing ratio between A and C will be in the same proportion as their old shares, since there is no information given about any changes in A's or C's share. Therefore, A's new profit share becomes 7 parts and C's share becomes 3 parts, for a new profit-sharing ratio of 7:3.
For the gaining ratio, it's the proportion in which the outgoing partner's share is distributed to the remaining partners. In this case, B's share (5 parts) needs to be distributed between A and C. There is no information about any agreement regarding the distribution of B's share; we assume that A and C will gain in proportion to their existing shares. Thus, A gains 7 parts of B's 5 shares, and C gains 3 parts. The gaining ratio of A and C is therefore calculated as the ratio of their gains, which is 7:5.