Question

A & B are partners sharing profits and losses in the ratio of 3 : 2. C is admitted for `1/4` share and for which ₹ 30,000 and ₹ 10,000 are credited as a premium for goodwill to A and B, respectively. The new profit sharing ratio of A : B : C will be ______.

Options

• 3 : 2 : 1

• 12 : 8 : 5

• 9 : 6 : 5

• 33 : 27 : 20

Answer 1

A & B are partners sharing profits and losses in the ratio of 3 : 2. C is admitted for `1/4` share and for which ₹ 30,000 and ₹ 10,000 are credited as a premium for goodwill to A and B, respectively. The new profit-sharing ratio of A : B : C will be 33 : 27 : 20.

Explanation:

The ratio in which the goodwill premium is shared is the sacrificing ratio.

Sacrificing Ratio of A and B = 30,000 : 10,000

= 3 : 1

Calculate the Sacrificed Share of each partner:

C is admitted for a `1/4` share, which is the total share sacrificed by A and B in their 3 : 1 ratio.

A’s Sacrificed = `1/4 xx 3/4`

= `3/16`

B’s Sacrificed = `1/4 xx 1/4`

= `1/16`

Calculate the New Share of each partner:

New Share = Old Share − Sacrificed Share

A’s New Share = `3/5 - 3/16`

= `(3 xx 16)/(5 xx 16) - (3 xx 5)/(16 xx 5)`

= `48/80 - 15/80`

= `33/80`

B’s New Share = `2/5 - 1/16`

= `(2 xx 16)/(5 xx 16) - (1 xx 5)/(16 xx 5)`

= `32/80 - 5/80`

= `27/80`

C’s New Share = `1/4`

= `(1 xx 20)/(4 xx 20)`

= `20/80`

The new profit-sharing ratio of A, B, and C = `33/80 : 27/80 : 20/80` or 33 : 27 : 20