Kaushal and Gulab are partners in a firm sharing profits in the ratio of 5: 3. They admit Raju as a new partner for 1/7 share in the profit. The new profit sharing ratio will be 4:2:1. The sacrificing ratio of Kaushal and Gulab will be:

Question

Accepted Answer

The correct option is 1:

The correct answer is determined by applying the fundamental accounting formula for the Sacrificing Ratio, which is essential upon the admission of a new partner. The formula is: Sacrificing Share = Old Share - New Share. In this case, the old partners, Kaushal and Gulab, must give up a portion of their existing profit share to accommodate Raju. Kaushal's Old Share is 5/8, and his New Share is 4/7. His sacrifice is calculated as (5/8) - (4/7) = (35 - 32) / 56 = 3/56. Similarly, Gulab's Old Share is 3/8, and his New Share is 2/7. His sacrifice is calculated as (3/8) - (2/7) = (21 - 16) / 56 = 5/56. Therefore, the sacrificing ratio is 3/56 : 5/56, which simplifies to the ratio 3:5.

The incorrect option is 2:
This ratio (5:3) represents the original, old profit-sharing ratio between Kaushal and Gulab. While the old ratio is a component of the calculation, it is not the sacrificing ratio itself. The sacrificing ratio is only equal to the old ratio when the new partner acquires their share from the old partners in a manner that maintains the *relative* proportions of the old partners' shares, and crucially, when the new profit-sharing ratio is *not* specifically given. Since the new ratio (4:2:1) *is* provided, we must calculate the exact sacrifice made by each partner, which proves to be 3:5.

The incorrect option is 3:
This ratio (4:2) is the simplified ratio of the old partners' shares in the *new* profit-sharing arrangement (4/7 : 2/7). This ratio reflects the partners' future entitlements to profit but does not measure the actual *reduction* in their shares. The sacrificing ratio measures the loss or surrender of profit share, while the new ratio measures the eventual distribution of profit. Hence, simply taking the new ratio of the old partners will yield an incorrect result for the sacrifice calculation.

The incorrect option is 4:
This ratio (1:7) is derived from the new partner Raju's share (1/7). It is not a ratio of sacrifice between the old partners. The share of a new partner is the total amount sacrificed by the existing partners combined, but this option incorrectly presents Raju's share as a ratio between Kaushal and Gulab. Ratios like 1:7 or 7:1 are entirely irrelevant in the determination of the sacrificing ratio between the two original partners.