A and B are sharing profits in the ratio of 3: 2. They admit C as a new partner with 1/5th share in the profits which he gets equally from A and B. Calculate the new profit sharing ratio:

Question

Accepted Answer

The correct option is 2:
When a new partner is admitted, the first crucial step is to determine the sacrificing shares of the old partners. The question states that the new partner, C, acquires his 1/5th share *equally* from partners A and B. This means both A and B sacrifice 1/2 of C's share. The amount sacrificed by A is (1/5) \* (1/2) = 1/10, and similarly, the amount sacrificed by B is (1/5) \* (1/2) = 1/10. To calculate the new profit sharing ratio, we must subtract the sacrificed share from the old share of each partner. A's new share is (3/5) - (1/10) = (6/10) - (1/10) = 5/10. B's new share is (2/5) - (1/10) = (4/10) - (1/10) = 3/10. C's share, 1/5, is equivalent to 2/10. Therefore, the new profit sharing ratio for A:B:C is 5/10 : 3/10 : 2/10, or 5:3:2.

The incorrect option is 1:
This option, 3:1:5 (or 3/9:1/9:5/9), is incorrect as it fails to properly account for the sacrifice of shares. If the ratio were 3:1:5, it would imply C has a 5/9th share, which is much larger than the given 1/5th share. Furthermore, the old partners' share of 3/5 and 2/5 are not maintained proportionally to the initial terms after C's 1/5th share acquisition. This ratio is numerically inconsistent with the calculated reduction in A and B's shares.

The incorrect option is 3:
This option, 2:1:5 (or 2/8:1/8:5/8), is incorrect. As in option 1, this ratio also assumes an incorrect share for the new partner C (5/8, which is far more than the given 1/5) and a significantly altered relationship between the old partners. It completely deviates from the rule of deducting the specific sacrifice (1/10 each) from the old ratio (3/5 and 2/5). A new ratio of 2:1 for A and B would imply a much larger sacrifice than 1/10 by A.

The incorrect option is 4:
This option, 5:3:1 (or 5/9:3/9:1/9), is incorrect because it misstates the new partner C's final share. While the new shares for A (5/10) and B (3/10) are correctly proportional (5:3), C's new share is 1/5, which is 2/10. This option incorrectly assigns C a share of 1/9 (or 1/10 in the ratio breakdown), thus reducing C's entitlement and preventing the total share from summing up to unity (1).