Step 1: Recall the rule:
Continuing partners gain the retiring partner's share. When no agreement is mentioned, the default rule is to share the gain in proportion to their existing shares.
Step 2: Test with a small example:
Let A, B and C share profits in the ratio 5:3:2, and let C retire. C's share is 2/10. If nothing is said, A and B take it in the ratio 5:3. A gains 2/10 x 5/8 = 1/8 and B gains 2/10 x 3/8 = 3/40.
Step 3: Find the new shares:
A's new share = 5/10 + 1/8 = 5/8. B's new share = 3/10 + 3/40 = 3/8. So A and B now share 5:3, the same relative ratio as before. The old ratio among the continuing partners is preserved.
Step 4: Rule out the other choices:
The new ratio is the outcome, not the input, so it cannot be the basis. An equal split changes the relative position of the partners without any agreement to do so. A ratio that is profitable to them is not a legal or accounting basis at all.
Step 5: Conclusion:
Only the old profit sharing ratio matches the default rule. This is option 1.
Final Answer:
The remaining partners acquire the share in the old profit sharing ratio, so option 1 is correct.
\[ \boxed{\text{Old Profit Sharing Ratio (Option 1)}} \]