The retiring partner is entitled to his share of goodwill at the time of retirement because goodwill has been earned by the firm through the efforts of all existing partners. If goodwill does not appear in the firm's books of accounts, the correct journal entry for treatment of goodwill in this case is:

Gaining Partners' Capital A/c Dr.
To Retiring Partners' Capital A/c
(Share in goodwill of retiring partner adjusted)

Correct answer: Option (1) → Gaining Partners' Capital A/c Dr.; To Retiring Partners' Capital A/c; (Share in goodwill of retiring partner adjusted)

Concept: When goodwill does not appear in the books, the retiring partner’s share of goodwill is adjusted through the capital accounts – the gaining partners are debited and the retiring partner credited, in the gaining ratio – per Reconstitution of a Partnership Firm – Retirement/Death of a Partner.

The continuing (gaining) partners acquire the retiring partner’s share, so they compensate him: Gaining Partners’ Capital A/c Dr. To Retiring Partner’s Capital A/c. Goodwill is NOT raised in the books (no Goodwill A/c is opened), which rules out the other entries.