Question

A and B are partners sharing profits and losses in the ratio of $3:2$. They admit C into the partnership for one-fourth share of the profits while A and B as between themselves are sharing profits & losses equally. The new profit sharing ratio will be _______.

• A. NR $3:3:2$, SR $1:9$
• B. NR $4:2:2$, SR $9:1$
• C. NR $3:3:2$, SR $9:1$
• D. None of these

Answer 1

The correct option is C NR $3:3:2$, SR $9:1$

Old ratio (A and B) = 3 : 2

C is admitted for 1/4 share

Let the combined share of A, B and C = 1

Combined share of A and B after C's admission = 1 - C's share

= 1 - (1/4) = 3/4

New share :

A = (3/4) * (1/2) = 3/8

B = (3/4) * (1/2) = 3/8

C = 1/4

Therefore, A : B : C = 3/8 : 3/8 : 1/4

= 3 : 3 : 2

Sacrificing ratio = Old ratio - New ratio

A's sacrifice = (3/5) - (3/8) = 9/24

B's sacrifice = (2/5) - (3/8) = 1/24

Therefore, sacrificing ratio of A and b is 9 : 1