A and B are partners sharing profit in the ratio of 7:3 C was admitted...
Calculation of Sacrificing Ratio:
Sacrificing ratio refers to the ratio in which the existing partners are willing to sacrifice their share of profit in favour of the incoming partner.
Let the total profit be x.
Before the admission of C, the profit sharing ratio of A and B was 7:3. Therefore, A's share of profit was (7/10)x and B's share was (3/10)x.
After the admission of C, A surrendered 1/7th of his share and B surrendered 1/3rd of his share in favour of C.
Therefore, the new share of A in the profit will be ((6/7) x (7/10)) = (6/10)x and the new share of B will be ((2/3) x (3/10)) = (2/10)x.
The share of C will be ((1/7) + (1/3))x = (10/21)x.
The sacrificing ratio of A and B can be calculated as follows:
A's sacrifice = (7/10)x - (6/10)x = (1/10)x
B's sacrifice = (3/10)x - (2/10)x = (1/10)x
Therefore, the sacrificing ratio of A and B is 1:1.
Calculation of New Profit Sharing Ratio:
The new profit sharing ratio after the admission of C can be calculated as follows:
A's new share = (6/10)x
B's new share = (2/10)x
C's share = (10/21)x
The total profit sharing ratio = (6/10) + (2/10) + (10/21) = (63/70)
Therefore, the new profit sharing ratio of A, B, and C will be:
A = ((6/10)/(63/70)) = (12/21) or (4/7)
B = ((2/10)/(63/70)) = (4/21)
C = ((10/21)/(63/70)) = (10/63)
A and B are partners sharing profit in the ratio of 7:3 C was admitted...