Question

A and B were partners sharing profits in the ratio of 21 : 9. C was admitted on `9/21` share in the profits. Calculate new profit sharing ratio of the partners.

Answer 1

Let total profit be = 1.

Share given to C = `9/21`

Remaining Share = `1 - 9/21`

= `12/21`

= `4/7`

Now the old partners will share this remaining profit in their old profit sharing ratios:

The old ratio A : B = 21 : 9, which simplifies to 7 : 3 (dividing both by 3).

Hence,

A’s Share = `4/7 xx 7/10`

= `28/70`

= `2/5`

B’s Share = `4/7 xx 3/10`

= `12/70`

= `6/35`

C’s Share = `9/21`, which simplifies to `3/7`

To get the ratio, find a common denominator for the shares of A, B, and C.

A’s new share = `2/5 xx 7/7`

= `14/35`

B’s new share = `6/35`

C’s new share = `3/7 xx 5/5`

= `15/35`

The new profit-sharing ratio for A, B, and C is `14/35 : 6/35 : 15/35` or 14 : 6 : 15.