Question

A and B share profits in the ratio of 2 : 1. C is admitted with `1/4` a share in profits. C acquires `3/4` of his share from A and `1/4` of his share from B. The new ratio will be ______.

Options

• 2 : 1 : 1

• 23 : 13 : 12

• 3 : 1 : 1

• 13 : 23 : 12

Answer 1

A and B share profits in the ratio of 2 : 1. C is admitted with `1/4` a share in profits. C acquires `3/4` of his share from A and `1/4` of his share from B. The new ratio will be 23 : 13 : 12.

Explanation:

C's share is `1/4`. C acquires `3/4` of his share from A and `1/4` of his share from B.

A’s sacrifice = `1/4 xx 3/4`

= `3/16`

B’s sacrifice = `1/4 xx 1/4`

= `1/16`

Calculate the new share of each partner.

The old ratio of A and B is 2 : 1, so their shares are `2/3` and `1/3`. The new share is calculated by subtracting the sacrificed share from the old share.

A’s new share = `2/3 - 3/16`

= `(2 xx 16)/(3 xx 16) - (3 xx 3)/(16 xx 3)`

= `32/48 - 9/48`

= `23/48`

B’s new share = `1/3 - 1/16`

= `(1 xx 16)/(3 xx 16) - (1 xx 3)/(16 xx 3)`

= `16/48 - 3/48`

= `13/48`

C’s share = `1/4`

= `(1 xx 12)/(4 xx 12)`

= `12/48`

The new profit-sharing ratio for A, B, and C = `23/48 : 13/48 : 12/48` or 23 : 13 : 12.