At the time of admission of a partner, if nothing is specified then n…

The correct answer is Option (2) → In Old Profit Sharing Ratio

When a new partner comes in, the old partners give up (sacrifice) a part of their shares for him. If the partners have not agreed on how this is to be shared, it is assumed that the old partners give it up in the same ratio in which they were sharing profits, that is, in their old profit sharing ratio.

Option (1) In New Profit Sharing Ratio — Incorrect. The new ratio is the result. It is worked out after knowing how much each old partner gives up, so it cannot be the basis for that sacrifice.

Option (2) In Old Profit Sharing Ratio — Correct. With no agreement, the old partners keep their relative positions and sacrifice in the old ratio.

Option (3) In Gaining Ratio — Incorrect. The gaining ratio is the ratio in which continuing partners gain the share of a retiring or deceased partner. On admission nobody gains among the old partners; they only sacrifice.

Option (4) In Sacrificing Ratio — Incorrect. The sacrificing ratio is the very ratio being worked out here, so it cannot be its own basis. When nothing is agreed, the sacrificing ratio is taken to be the same as the old ratio, so the basis is the old profit sharing ratio.