If the new partner brings goodwill in cash and the amount is retained in the firm on what basis will old partners' capital accounts be credited?

Correct answer: Sacrificing ratio

The direct answer is option A: the sacrificing ratio. When a new partner enters, the old partners give up part of their future profit share for the new partner. This reduction is called sacrifice. Goodwill brought in cash by the new partner is compensation for that sacrifice, so the amount retained in the firm is credited to the old partners in the ratio in which they sacrifice profit. The steps are: find each old partner’s old share; find the new share after admission; calculate sacrifice as old share minus new share; distribute the goodwill contribution to old partners in that sacrificing ratio. Option A is correct. Option B, new ratio, shows how profits will be shared after admission, not how the old partners gave up their shares. Option C, equal ratio always, is wrong because sacrifice is not automatically equal; it depends on the actual old and new ratios. Option D, capital ratio, is wrong because goodwill compensation is linked to profit sacrifice, not to the amounts of capital contributed. For example, if two old partners sacrifice in the ratio 2:1, goodwill cash is credited to them in 2:1, even if their capitals are unequal. The exam cue is: admission means old partners sacrifice; retirement or death often involves gaining partners. Use the ratio connected with the event, not a convenient but unrelated capital ratio.