When A and B, the existing partners, decide to admit C into their partnership, certain calculations need to be made to determine the new profit-sharing ratio and the sacrificing ratio. Here’s how we can approach this problem:
1. Initial Ratios:
A and B share profits and losses in the ratio of 3:2.
– Total parts = 3 + 2 = 5.
– A’s share = 3/5
– B’s share = 2/5
2. Admission of Partner C:
– C is admitted for a 1/4 share (or 25%) of the profits.
3. Calculation of New Shares:
– Since C is entitled to 1/4 of the profits, we must first convert this into a format that fits with the existing ratio.
– Total profit share now is represented in parts. Thus, if C takes 1/4, that leaves A and B with a combined share of 3/4.
4. Existing Shares After C’s Admission:
– The remaining share for A and B will be:
Combined share of A and B = 1 – 1/4 = 3/4.
– A and B need to adjust their shares so that their total adds up to 3/4 of the profit.
5. Conversion of Existing Shares to New Ratio:
– We must now express A and B’s shares in terms of the remaining 3/4.
– To do this, we take their existing shares and divide them by the total (3/5) then multiply by 3/4.
– A’s new share:
A’s new share = (3/5) * (3/4) = 9/20.
– B’s new share:
B’s new share = (2/5) * (3/4) = 6/20.
6. New Profit-sharing Ratio:
– Thus, the new profit-sharing ratio among A, B, and C will now be:
– A : B : C = 9/20 : 6/20 : 5/20,
which simplifies to 9:6:5.
7. Calculation of Sacrificing Ratio:
– To find the sacrificing ratio, we need to determine how much A and B have sacrificed from their original ratios to accommodate C.
– A’s sacrifice = Original share – New share = 3/5 – 9/20 = 12/20 – 9/20 = 3/20.
– B’s sacrifice = Original share – New share = 2/5 – 6/20 = 8/20 – 6/20 = 2/20.
– The sacrificing ratio, therefore, is A’s sacrifice : B’s sacrifice = 3 : 2.
In summary:
– New Profit-Sharing Ratio: 9:6:5
– Sacrificing Ratio: 3:2