Question

A and B share profits and losses in the ratio of 3 : 2. They admit C as a new partner for `1/3`rd share in the profits of the firm which he acquired from A and B in the ratio of 2 : 3. After some time, they admitted D as a new partner for `1/5`th share in the profits which he acquired equally from A and C.

Calculate:

1. New profit sharing ratio of A, B and C;
2. New profit sharing ratio of A, B, C and D.

Answer 1

(i) Calculation of New Profit Sharing Ratio of A, B and C:

Share of Profit given to C = `1/3`

Share acquired by C from A = `2/5 xx 1/3`

= `2/15`

Share acquired by C from B = `3/5 xx 1/3`

= `3/15`

Hence, A’s new share = `3/5 - 2/15`

= `(3 xx 3)/(5 xx 3) - 2/15`

= `9/15 - 2/15`

= `7/15`

B’s new share = `2/5 - 3/15`

= `(2 xx 3)/(5 xx 3) - 3/15`

= `6/15 - 3/15`

= `3/15`

C’s new share = `1/3`

= `(1 xx 5)/(3 xx 5)`

= `5/15`

Thus, New Profit Sharing Ratio among A, B, and C = `7/15 : 3/15 : 5/15` or 7 : 3 : 5

(ii) Calculation of New Profit Sharing Ratio of A, B, C and D:

Share of Profit given to D = `1/5`

Share acquired by D from A = `1/2 xx 1/5`

= `1/10`

Share acquired by D from C = `1/2 xx 1/5`

= `1/10`

Hence, A’s new share = `7/15 - 1/10`

= `(7 xx 2)/(15 xx 2) - (1 xx 3)/(10 xx 3)`

= `14/30 - 3/30`

= `(14 - 3)/30`

= `11/30`

B’s new share = `3/15`

= `(3 xx 2)/(15 xx 2)`

= `6/30`

C’s new share = `5/15 - 1/10`

= `(5 xx 2)/(15 xx 2) - (1 xx 3)/(10 xx 3)`

= `10/30 - 3/30`

= `(10 - 3)/30`

= `7/30`

D’s new share = `1/5`

= `(1 xx 6)/(5 xx 6)`

= `6/30`

Thus, New Profit Sharing Ratio among A, B, C, and D = `11/30 : 6/30 : 7/30 : 6/30` or 11 : 6 : 7 : 6