Question

Nastration 1 (New Partner's Share is given but Sacrifices made by Old Partners are not given)
A and B are partners sharing profits in the ratio of 5 : 3. C is admitted for 1/4th share in
Calculate New Profit-sharing Ratio of the partners
the profits​

Answer 1

Old ratio (A and B) = 5 : 3

C is admitted for 3/10th share of profit

A's sacrifice in favour of C = 1/5

B's sacrifice in favour of C = 1/10

New ratio = Old ratio - Sacrifcing ratio

A's new ratio = (5/8) - (1/5) = 17/40

B's new ratio = (3/8) - (1/10) = 11/40

C's share = 3/10 or 12/40

Therefore, new profit sharing ratio of A : B : C is 17 : 11 : 12

Answer 2

Calculation of New - profit sharing ratio:

Old profit sharing ratio of A and B = $\sf{5:3 \: or \: \frac{5}{8} \: : \: \frac{3}{8}}$

Let the total profit = 1,

C's profit share = $\sf{\frac{1}{4}}$

Remaining profit share of A and B = $\sf{1 - \frac{1}{4} = \frac{3}{4} }$

Distribute the remaining share of $\frac{3}{4} th$

in the old profit sharing ratio of 5:3 between A and B.

A's profit share = $\frac{3}{4} \times \frac{5}{8} = \frac{15}{32}$

B's profit share = $\frac{3}{4} \times \frac{3}{8} = \frac{9}{32}$

C's profit share = $\frac{1}{4} \: or \: \frac{8}{32}$

Thus, new profit sharing ratio of A,B and C = $\frac{15}{32} : \frac{9}{32} : \frac{8}{32} = 15:9:8$