Question

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

Answer 1

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

Solution :-

given that,

→ A : B = 7 : 5

so,

→ A share = 7/(7 + 5) = (7/12) of total .

→ B share = 5/(7 + 5) = (5/12) of total .

given that, for managing ,

→ C gets = (1/24) from A .

so,

→ A share left = (7/12) - (1/24) = (14 - 1)/24 = (13/24) .

and,

→ C gets = (1/8) from B .

so,

→ A share left = (7/12) - (1/8) = (14 - 3)/24 = (11/24) .

given that,

→ C gets = (1/6) of total profit .

therefore,

→ New profit sharing of A : B : C = (13/24) : (11/24) : (1/6) = (13 : 11 : 4)/24 = 13 : 11 : 4 (Ans.)

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Answer 2

Explanation:

Solution :

Old Ratio:

A : B = 7 : 5

A 's Share = $\frac{7}{12}$

B's Share = $\frac{5}{12}$

They agree to admit C, their manager, into partnership who is to get 1/6th share in the profits.

C acquired 1/24 th from A

C acquired 1/8 th from B

A's new share =

$= \frac{7}{12} - \frac{1}{24} = \frac{14 - 1}{24} = \frac{13}{24}$

B's new share =

$= \frac{5}{12} - \frac{1}{8} = \frac{10}{24} - \frac{3}{24} = \frac{7}{24}$

C's share =

$= \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}$

A:B:C = $= \frac{13}{24} : \frac{7}{24} : \frac{4}{24}$

Hence, new Profit Sharing ratio = A:B:C = 13:7:4