Question

A and B are partners sharing profits and losses in the ratio of 7 : 5. They agree to admit C, their manager, into the partnership, who is to get `1/6`th share in the profits. He acquires this share as `1/24`th from A and `1/8`th from B. The new profit-sharing ratio will be ______.

Options

• 13 : 7 : 4

• 7 : 13 : 4

• 7 : 5 : 6

• 5 : 7 : 6

Answer 1

A and B are partners sharing profits and losses in the ratio of 7 : 5. They agree to admit C, their manager, into the partnership, who is to get `1/6`th share in the profits. He acquires this share as `1/24`th from A and `1/8`th from B. The new profit-sharing ratio will be 13 : 7 : 4.

Explanation:

Old Ratio of  A and B = 7 : 5
C admits for `1/6` share of Profit

A sacrifices his share of profit in favour of C = `1/24`

B sacrifices his share of profit in favour of C = `1/8`

New Ratio = Old Ratio − Sacrificing Ratio

A’s = `7/12 - 1/24`

= `(7 xx 2)/(12 xx 2) - 1/24`

= `14/24 - 1/24`

= `13/24`

B’s = `5/12 - 1/8`

= `(5 xx 2)/(12 xx 2) - (1 xx 3)/(8 xx 3)`

= `10/24 - 3/24`

= `7/24`

C’s share = `1/6`

= `(1 xx 4)/(6 xx 4)`

= `4/24`

New Profit Sharing Ratio of  A, B, and  C = `13/24 : 7/24 : 1/6` or 13 : 7 : 4.