Question

B and N are partners in a firm sharing profits in the ratio of 3 : 2. They admit S as a partner for `1/4`th share in the profits. S acquires his share from B and N in the ratio of 2 : 1. The new profit-sharing ratio will be ______.

Options

• 2 : 1 : 4

• 19 : 26 : 15

• 3 : 2 : 4

• 26 : 19 : 15

Answer 1

B and N are partners in a firm sharing profits in the ratio of 3 : 2. They admit S as a partner for `1/4`th share in the profits. S acquires his share from B and N in the ratio of 2 : 1. The new profit-sharing ratio will be 26 : 19 : 15.

Explanation:

Calculate the sacrifice of each partner.

S is admitted for a `1/4` share. He acquires this share from B and N in the ratio of 2 : 1.

B’s sacrifice = `1/4 xx 2/3`

= `2/12`

N’s sacrifice = `1/4 xx 1/3`

= `1/12`

Calculate the new share of each partner.

The old ratio of B and N is 3 : 2.

B’s new share = `3/5 - 2/12`

= `(3 xx 12)/(5 xx 12) - (2 xx 5)/(12 xx 5)`

= `36/60 - 10/60`

= `26/60`

N’s new share = `2/5 - 1/12`

= `(2 xx 12)/(5 xx 12) - (1 xx 5)/(12 xx 5)`

= `24/60 - 5/60`

= `19/60`

S’s share = `1/4`

= `(1 xx 15)/(4 xx 15)`

= `15/60`

New profit-sharing ratio for B, N, and S = `26/60 : 19/60 : 15/60` or 26 : 19 : 15.