Question

S, T and U were partners in a firm. They admitted V as a new partner. S and T sacrificed `1/3`rd and `1/4`th of their share, respectively, in favour of V. Calculate the new profit-sharing ratio of S, T, U and V.

Answer 1

In the absence of a stated profit-sharing ratio among partners, it is assumed that they share profits and losses equally. This assumption is based on the provisions of the Indian Partnership Act, 1932.

S’s old share = `1/3`

S’s new share = `1/3 - 1/9`

= `(1 xx 3)/(3 xx 3) = 3/9`

= `3/9 - 1/9`

= `2/9`

T’s old share = `1/3`

Sacrifice by T = `1/3 xx 1/4`

= `1/12`

T’s new share = `1/3 - 1/12`

= `(1 xx 4)/(3 xx 4)`

= `4/12`

= `4/12 - 1/12`

= `3/12`

= `1/4`

U’s new share = U did not sacrifice any share, so his share remains `1/3`.

V’s share is the sum of the sacrifices made by S and T.

V’s share = Sacrifice by S + Sacrifice by T

V’s share = `1/9 + 1/12`

= `(4 + 3)/36`

= `7/36`

To find the ratio, find a common denominator, which is 36.

S = `2/9`

= `(2 xx 4)/(9 xx 4)`

= `8/36`

T = `1/4`

= `(1 xx 9)/(4 xx 9)`

= `9/36`

U = `1/3`

= `(1 xx 12)/(3 xx 12)`

= `12/36`

V = `7/36`

The new profit-sharing ratio of `8/36 : 9/36 : 12/36 : 7/36` or 8 : 9 : 12 ; 7