The correct answer is option 3- (A)-(I), (B)-(II), (C)-(IV), (D)-(III).
| LIST I |
LIST II |
| (A) Gaining Ratio |
(I) New Share - old Share |
| (B) Sacrificing Ratio |
(II) Old Share - New Share |
| (C) Admission of Partner |
(IV) Partner may or may not bring his share of goodwill in cash |
| (D) Retirement of Partner |
(III) Partner may be paid amount more that what
has actually due to him for hidden goodwill |
(A) Gaining Ratio- (I) New Share - old Share.
When a partner retires from a partnership, the gaining ratio is used to determine the new profit-sharing ratio among the remaining partners. The gaining ratio is calculated by deducting old ratio from new ratio.
(B) Sacrificing Ratio- (II) Old Share - New Share.
The sacrifice ratio is the ratio in which existing partners agree to reduce their shares in favor of the new partner. It is calculated by deducting new new ratio from old ratio.
(C) Admission of Partner- (IV) Partner may or may not bring his share of goodwill in cash.
When a new partner is admitted, they might contribute goodwill (a premium for joining an established firm), but it is not mandatory that this is brought in cash—it can be adjusted through the new partner current account.
(D) Retirement of Partner- (III) Partner may be paid amount more that what has actually due to him for hidden goodwill.
On retirement, a partner may receive an amount over and above his capital and share of profits, which accounts for hidden goodwill (not recorded in the books but valued implicitly). | 
